Appendix F: Answers to Selected Exercises
This appendix provides worked solutions and detailed guidance for selected exercises throughout the book. Calculation-based exercises show every step; conceptual exercises describe what a well-reasoned answer includes. Inspection exercises describe what a typical older home will reveal and what findings mean.
Exercises are identified by chapter and number. Where an exercise has a range of valid answers depending on circumstances, guidance is given for the most common cases.
Chapter 1: How a House Is Built
Exercise 1.2: Identifying Trades on a Construction Schedule Answer: The correct sequence for the trades involves dependencies that are easy to miss. Foundation work must complete and cure before framing. Framing must be fully erected, braced, and inspected before rough-in trades begin. Rough mechanical trades (plumbing, electrical, HVAC) must complete rough-in before insulation. Insulation must be inspected before drywall. Drywall must be hung and finished before flooring and most trim. Painting typically follows drywall finishing and precedes finish plumbing and electrical trim. Final plumbing, electrical, and HVAC trim come after flooring and paint. The certificate of occupancy inspection is last.
A common error is placing insulation before electrical rough-in, or flooring before drywall finishing. Both create expensive rework.
Exercise 1.4: Load Path Tracing Answer: For a two-story house with an attic, the load path from a ridge beam is: ridge beam → rafters → top plate of exterior wall → studs → bottom plate → floor sheathing → floor joists → beam or girder → post or bearing wall → foundation wall → footing → soil. Each transfer point must be engineered to handle the cumulative load above it. At any point where a connection is missing or undersized — a joist hanger pulled out, a post not bearing on a beam — the load path is broken.
Chapter 2: Foundations
Exercise 2.1: Identifying Your Foundation Type Answer (inspection guidance): To identify your foundation type, access the perimeter of the building from the exterior or from a basement/crawlspace. A slab-on-grade will show no accessible space below the floor; the floor structure is the concrete slab itself. A crawlspace will be accessible through a hatch and will show floor joists overhead and a soil floor (or encapsulated vapor barrier) below, typically 18–48 inches of clearance. A full basement will have a full-height (typically 7+ foot) enclosed space below. Partial basements may combine a basement section with a crawlspace section under additions. Piers or posts supporting floor beams visible in a crawlspace indicate the house is on piers rather than a continuous wall.
Exercise 2.3: Crack Classification Answer: Horizontal cracks in poured concrete or concrete block basement walls are serious — they indicate inward pressure from soil and water, which can lead to wall failure. They require structural engineering evaluation, not cosmetic repair.
Stair-step cracks in block or brick mortar joints indicate differential settlement. The severity depends on the size (small gaps vs. wide openings) and direction (converging at the top indicates rotation of one section).
Vertical hairline cracks in poured concrete walls are very common and typically result from concrete shrinkage during curing. Narrow hairline cracks (less than 1/8 inch) that are not actively leaking and show no evidence of water staining are generally cosmetic. Cracks wider than 1/4 inch or any crack with displacement (one side higher than the other) warrant professional evaluation.
Chapter 3: Framing
Exercise 3.2: Calculating Header Size Answer: Header sizing is governed by the span, the load above, and whether the wall is load-bearing. For a rough rule of thumb under typical residential loads, a 3-foot opening in a load-bearing wall requires a minimum 2-ply 2x6 header; a 4-foot opening requires 2x8; a 6-foot opening requires 2x10; and openings exceeding 6 feet typically require 2x12 or LVL, depending on load. Always confirm against the IRC span tables (Table R602.7 and related tables) for your specific conditions. In a non-load-bearing wall, a single flat 2x4 or 2x6 is acceptable for most openings.
Exercise 3.5: Identifying Load-Bearing Walls Answer (inspection guidance): Reliable indicators of a load-bearing wall: (1) The wall runs perpendicular (at 90 degrees) to the floor and ceiling joists above, meaning joists are bearing on it. (2) The wall sits directly above a beam, girder, or another bearing wall below. (3) The wall is at the center of the house and runs parallel to the ridge — a common configuration for a center bearing wall. (4) In the attic, the wall has a double top plate, and roof-framing members (rafters or a ridge beam) land on or just above it.
Non-indicators that people often mistakenly use: the wall is exterior (some exterior walls carry minimal vertical load), the wall is heavy or built of solid brick (masonry veneer is not structural), the wall has electrical outlets (wiring runs through all walls regardless of structure).
Chapter 4: Insulation and the Building Envelope
Exercise 4.1: R-Value Calculation — Wall Assembly Answer: Calculate total wall R-value by summing each component's R-value. For a typical 2x6 wood-framed wall:
| Component | R-value |
|---|---|
| Exterior air film | R-0.17 |
| Vinyl siding | R-0.61 |
| 1/2-inch OSB sheathing | R-0.63 |
| 5-1/2 inch fiberglass batt (2x6 cavity) | R-19 to R-21 |
| 1/2-inch drywall | R-0.45 |
| Interior air film | R-0.68 |
| Total (approximate) | R-21.5 to R-23.5 |
Note: This is the center-of-cavity R-value. The whole-wall R-value (accounting for thermal bridging through wood studs) is roughly 15–20% lower, typically in the R-17 to R-19 range for a standard 2x6 wall. Adding 1 inch of continuous exterior rigid foam insulation (R-5 to R-6) reduces thermal bridging significantly and is often the most cost-effective way to upgrade an existing wall.
Exercise 4.2: Insulation Upgrade Cost-Benefit Analysis Answer (worked example): Scenario: An attic currently has R-19 insulation (about 6 inches of blown fiberglass) and you are adding insulation to reach R-49 (approximately 15 inches total). The additional insulation needed has a material cost of approximately $0.50–$0.80 per square foot installed (blown cellulose or fiberglass, contractor-installed, typical 2025 pricing). For a 1,200 square foot attic:
- Cost to add insulation: 1,200 sq ft x $0.65 = approximately $780 (material and labor)
- Annual heating energy saved: The incremental benefit of R-19 to R-49 in a heating-dominated climate (approximately 5,000 heating degree days, natural gas at $1.20/therm) can be estimated as roughly 15–20% reduction in heating load, or approximately $80–$120 per year for a typical 1,500 sq ft home.
- Simple payback: $780 / $100 average annual savings = approximately 7–8 years.
This is a straightforward payback for a measure with a 30+ year service life. Paybacks shorten significantly with available rebates or tax credits (often 30% under current federal programs), improving to 5–6 years.
Exercise 4.3: Blower Door Test Interpretation Answer: A blower door result is expressed as ACH50 (air changes per hour at 50 Pascals of pressure). Common benchmarks:
- Greater than 7 ACH50: Very leaky; typical of pre-1980 housing with minimal air sealing
- 3–7 ACH50: Average existing housing stock
- 1–3 ACH50: Code-compliant new construction (2012+ IRC)
- Below 1 ACH50: Tight construction requiring mechanical ventilation (ASHRAE 62.2)
A house testing at 9 ACH50 is losing substantial heat through air infiltration and is a good candidate for air sealing work. A house testing at 0.6 ACH50 does not need additional air sealing but requires adequate mechanical ventilation to maintain air quality.
Chapter 5: Windows and Doors
Exercise 5.1: Reading a NFRC Label Answer: The NFRC (National Fenestration Rating Council) label on a window shows: U-factor (overall heat transfer; lower is better, aim for U-0.30 or below in cold climates), SHGC (Solar Heat Gain Coefficient; 0.0 to 1.0, where lower reduces solar gain — desirable in cooling climates, often desired higher in heating climates on south-facing windows), VT (visible transmittance; higher means more daylight), and air leakage (lower is better; maximum 0.3 cfm/sq ft is a common threshold).
A window labeled U-0.25, SHGC-0.27, VT-0.52 is a high-performance triple-pane unit suitable for a cold climate, with moderate solar gain and reasonable daylight.
Exercise 5.3: Window Replacement Cost-Benefit Answer: The honest calculation: Replacing double-pane windows (in reasonable condition) with new high-efficiency windows typically has a payback period of 25–50+ years based on energy savings alone, which often exceeds the product warranty period. The energy savings from improved windows are real but modest in most situations.
Where replacement makes financial sense: (1) Original single-pane windows with aluminum frames in cold climates, where the upgrade to double-pane low-e can genuinely reduce heating bills meaningfully. (2) Windows with failed seals (fogging between panes) where the insulating value has been lost. (3) Windows with severe air infiltration from failed weather-stripping that cannot be repaired. (4) When window replacement is combined with other envelope improvements as part of a deep energy retrofit.
Chapter 6: Water Supply
Exercise 6.2: Water Pressure Test Answer: Normal residential water pressure is 40–80 psi. To measure: attach a pressure gauge (available at hardware stores for under $15) to a hose bib or laundry connection. Measure static pressure (no water running) and flowing pressure (water running elsewhere in the house). Pressure consistently above 80 psi requires a pressure-reducing valve (PRV) to protect appliances and reduce pipe wear. Pressure below 40 psi indicates a problem with the supply, PRV setting, or branch line restriction. Pressure that fluctuates widely (e.g., drops sharply when a toilet is flushed) may indicate undersized supply pipes or high system demand.
Exercise 6.4: Pipe Material Identification Answer (inspection guidance): To identify pipe materials, look for exposed pipes at the water heater, in the basement or crawlspace ceiling, or under sinks. Copper: reddish-orange or brown-green (with patina), rigid, soldered fittings. CPVC: cream or light yellow rigid plastic, cemented fittings. PEX: flexible plastic tubing, red (hot) or blue (cold) or white, with crimp or push-fit fittings. Galvanized steel: silver-gray or rust-colored rigid pipe, threaded fittings. Polybutylene: gray flexible plastic, typically with gray or blue push-fit fittings — this is the problematic material that warrants replacement. If you find polybutylene, consult Chapter 6 for replacement guidance.
Chapter 7: Hot Water Systems
Exercise 7.1: Water Heater Recovery Time Calculation Answer: Recovery time is the time needed to heat a full tank from cold to set temperature. Formula: Recovery time (hours) = (Tank capacity in gallons × Temperature rise in °F × 8.33 BTU/gallon·°F) ÷ Burner BTU output
Example: 50-gallon gas water heater, incoming water at 55°F, setpoint 120°F, 40,000 BTU/hr burner: - Temperature rise: 120 - 55 = 65°F - BTU needed: 50 × 65 × 8.33 = 27,073 BTU - Recovery time: 27,073 ÷ 40,000 = 0.68 hours ≈ 41 minutes
A 50-gallon electric heater with a 4,500-watt element (15,355 BTU/hr) would take: 27,073 ÷ 15,355 = 1.76 hours ≈ 106 minutes.
This is why electric resistance water heaters are often replaced in high-demand households.
Exercise 7.3: Anode Rod Inspection Answer (inspection guidance): Remove the anode rod from the water heater (typically a 1-1/16-inch hex head on top of the unit, sometimes under a plastic cap). A new anode rod is approximately 3/4-inch diameter and 40–44 inches long. It should be replaced when: it has worn down to 1/2-inch diameter or less, the steel core is exposed, it has developed calcium deposits covering more than 6 inches of the rod, or the water smells of sulfur (indicating the anode is depleted and bacteria are growing). In a home with a water softener, check the anode every 1–2 years; softened water accelerates anode consumption.
Chapter 8: Drain-Waste-Vent System
Exercise 8.1: P-Trap Function Test Answer: To confirm a P-trap is functioning: look for the characteristic S-curve or P-curve in the drain pipe beneath a fixture. If a drain produces sewer odors but drains normally, the trap has either dried out (evaporated water seal) or been siphoned. For a seldom-used floor drain or utility sink, run a cup of water down the drain; if the odor disappears, the trap was dry and is now re-sealed. For a trap that repeatedly dries out, add a tablespoon of vegetable oil after filling — it floats on the water seal and reduces evaporation. Persistent sewer odors after confirming the trap has water indicate a vent problem requiring professional diagnosis.
Chapter 12: Electricity Basics
Exercise 12.1: Ohm's Law Applications Answer: Three fundamental relationships:
(a) A circuit breaker protecting a 120V circuit is rated at 15 amps. What is the maximum wattage the circuit can safely carry? Power = Voltage × Current = 120V × 15A = 1,800 watts. At 80% of rated capacity (the NEC continuous load limit): 1,800 × 0.80 = 1,440 watts maximum continuous load for a 15-amp, 120V circuit.
(b) A 1,200-watt hair dryer plugged into a 120V outlet draws how many amps? Current = Power ÷ Voltage = 1,200W ÷ 120V = 10 amps. This is 67% of a 15-amp circuit — acceptable.
(c) A 5,000-watt electric baseboard heater requires what voltage and amperage? If 240V: Current = 5,000W ÷ 240V = 20.8 amps, requiring a dedicated 30-amp circuit with 10-gauge wire. This is why electric baseboard cannot be added casually to existing circuits.
Exercise 12.2: Reading the Electric Meter Answer: On a digital meter, the display shows cumulative kilowatt-hours (kWh) consumed since installation. To calculate monthly consumption: record the meter reading on the first of the month, and again on the last day. Subtract the earlier reading from the later reading. Example: reading on March 1 = 14,823 kWh; reading on April 1 = 15,256 kWh. Monthly consumption: 15,256 - 14,823 = 433 kWh. Multiply by the rate on your bill (e.g., $0.13/kWh) to get the energy charge: 433 × $0.13 = $56.29 (before taxes and delivery charges).
Exercise 12.4: Calculating Annual Appliance Cost Answer: Formula: Annual cost = (Watts ÷ 1,000) × Hours per year × $/kWh
| Appliance | Watts | Hours/Year | $/kWh | Annual Cost |
|---|---|---|---|---|
| Refrigerator (older, 18 cu ft) | 150W average | 8,760 | $0.13 | **$171** | |
| LED light bulb (replaces 60W incandescent) | 9W | 2,000 | $0.13 | **$2.34** | |
| Incandescent 60W equivalent | 60W | 2,000 | $0.13 | **$15.60** | |
| Electric water heater (50-gal) | 4,500W | 876 (est. 3 hrs/day) | $0.13 | **$512** | |
| 65-inch LED TV | 110W | 1,460 (4 hrs/day) | $0.13 | **$20.90** |
The electric water heater is the largest single electrical load in many homes without electric heat. Upgrading to a heat pump water heater with COP of 3.5 would reduce that $512 to approximately $146/year — a savings of $366 annually.
Chapter 13: The Electrical Panel
Exercise 13.1: Circuit Capacity Calculation Answer: To calculate available circuit capacity and determine if a panel can support an addition:
Step 1 — Calculate existing connected load in volt-amps (VA): - General lighting and receptacles: 3 VA per square foot of living area (NEC standard method) - For a 1,400 sq ft house: 1,400 × 3 = 4,200 VA - Kitchen small appliance circuits: 2 × 1,500 VA = 3,000 VA - Laundry circuit: 1,500 VA - Other 240V loads: nameplate rating × voltage
Step 2 — Apply demand factors (NEC 220.42): The first 3,000 VA at 100%; remaining general lighting VA at 35%.
Step 3 — Sum all loads and compare to service size (amps × 240V).
Example: For a 100-amp service (24,000 VA total capacity), if calculated demand is 18,500 VA, remaining capacity is 5,500 VA or roughly 23 amps on a 240V circuit — enough for a heat pump water heater or small EV charger, but likely not a full 50-amp EV circuit. This calculation demonstrates why 100-amp service is often insufficient for electrification upgrades. A full load calculation following NEC Article 220 is required before adding significant electrical loads.
Exercise 13.3: Panel Mapping Answer (inspection guidance): When mapping an unlabeled panel, work systematically: (1) Turn all breakers on. (2) With a helper, trip each breaker one at a time and identify what goes dead (use a plug-in circuit tester or lamp in each outlet, check overhead lights). (3) Record on the panel directory. Common patterns in a typical 1,500 sq ft house: 15-amp circuits for bedrooms (1–2 circuits), living room, dining room; 20-amp circuits for bathrooms, kitchen small appliances (minimum 2 required by code), garage; 20-amp dedicated circuit for refrigerator; 20-amp or 15-amp for laundry lighting; 30-amp 240V for electric dryer; 50-amp 240V for electric range; 20-amp or 30-amp 240V for electric water heater. Note any double-tapped breakers (two wires on one terminal), which are a code violation in most cases.
Chapter 14: Wiring, Outlets, and Switches
Exercise 14.2: Wire Gauge Selection Answer: The National Electrical Code specifies minimum wire gauges based on circuit amperage. The most important residential relationships:
| Circuit Amperage | Minimum Wire Gauge | Common Use |
|---|---|---|
| 15 amp | 14 AWG | General lighting and receptacles |
| 20 amp | 12 AWG | Kitchen, bath, garage circuits |
| 30 amp | 10 AWG | Electric dryer, A/C unit |
| 40 amp | 8 AWG | Electric range, large HVAC |
| 50 amp | 6 AWG | Large electric range, EV charger |
The most dangerous mismatch is 14-gauge wire on a 20-amp breaker: the wire will overheat before the breaker trips. Always match wire gauge to breaker rating; if in doubt, larger wire is never wrong.
Chapter 15: Lighting
Exercise 15.1: Lumens vs. Watts Comparison Answer: The old metric of watts-as-brightness no longer applies with LEDs. The relevant comparison:
| Old Incandescent | Equivalent Lumens | LED Wattage Required |
|---|---|---|
| 40W | ~450 lm | 6–8W |
| 60W | ~800 lm | 8–10W |
| 75W | ~1,100 lm | 11–13W |
| 100W | ~1,600 lm | 14–17W |
For room lighting design: a common rule of thumb is 20–30 lumens per square foot for general ambient lighting in a living space. A 150 sq ft bedroom at 25 lumens/sq ft requires approximately 3,750 lumens total — achievable with about four 800-lumen (60W equivalent) fixtures or recessed lights.
Chapter 17: Solar, EV Chargers, and Generators
Exercise 17.1: Solar System Sizing Answer: Rough sizing calculation for a rooftop solar system:
Step 1 — Determine annual electricity consumption. From your electric bills, sum 12 months of kWh usage. Example: 9,600 kWh/year.
Step 2 — Determine peak sun hours for your location. This varies from approximately 3.5 hours/day (Seattle) to 5.5 hours/day (Phoenix). Use 4.5 hours/day for a mid-latitude location.
Step 3 — Account for system efficiency losses (typically 80% of rated output reaches the grid, due to temperature, wiring, inverter losses).
Step 4 — Size in kilowatts: System size (kW) = Annual kWh ÷ (365 days × peak sun hours × 0.80) = 9,600 ÷ (365 × 4.5 × 0.80) = 9,600 ÷ 1,314 = 7.3 kW system
At approximately 350 watts per panel, this requires roughly 21 panels. At $3.00/watt installed (typical 2025 range is $2.50–$3.50/W after 30% federal tax credit): 7,300W × $3.00 = $21,900 installed.
Exercise 17.2: Solar Payback Calculation Answer: Using the 7.3 kW system above:
- Annual production: 9,600 kWh (sized to offset full usage)
- **Annual savings at $0.13/kWh (buyback or avoided purchase):** 9,600 × $0.13 = $1,248/year
- Net system cost after 30% federal tax credit: $21,900 × 0.70 = $15,330
- Simple payback: $15,330 ÷ $1,248 = 12.3 years
Payback improves significantly if: your utility rate is higher (common in Northeast and California at $0.20–$0.30/kWh), you have net metering at retail rate, or state/utility rebates apply. Payback extends if: your production estimate was optimistic, roof shading reduces output, or electricity rates fall. At $0.22/kWh average rate: savings = $2,112/year, payback = 7.3 years.
Exercise 17.4: EV Charger Electrical Requirements Answer:
| Level | Voltage | Amperage | Circuit Required | Miles Added/Hour |
|---|---|---|---|---|
| Level 1 | 120V | 12A | Standard 15A outlet | 3–5 miles |
| Level 2 (32A) | 240V | 32A | 40A dedicated circuit, 8 AWG | 20–25 miles |
| Level 2 (48A) | 240V | 48A | 60A dedicated circuit, 6 AWG | 30–35 miles |
For most homeowners driving 30–40 miles per day, a Level 2 32-amp charger (adding 20–25 miles per hour) fully charges most EVs overnight. The electrical requirement — a 240V, 40-amp circuit with 8-gauge wire to the garage — is a straightforward job for a licensed electrician, typically costing $400–$800 depending on panel location and run distance.
Chapter 18: Heating Systems
Exercise 18.1: Furnace Efficiency Comparison — Operating Cost Answer: Comparing an 80% AFUE furnace to a 96% AFUE furnace:
Scenario: Annual heating load of 80 million BTU (typical 2,000 sq ft home in a cold climate); natural gas at $1.20/therm (100,000 BTU).
- 80% AFUE furnace gas required: 80,000,000 ÷ 0.80 = 100,000,000 BTU input = 1,000 therms/year
- 96% AFUE furnace gas required: 80,000,000 ÷ 0.96 = 83,333,333 BTU input = 833 therms/year
- Annual savings: (1,000 - 833) therms × $1.20 = 167 × $1.20 = $200/year
- Additional cost of 96% vs. 80% AFUE unit: approximately $400–$700 more at installation
- Simple payback on efficiency upgrade: $550 ÷ $200 = 2.75 years — an excellent return.
Exercise 18.3: Heat Pump Balance Point Answer: The balance point is the outdoor temperature at which a heat pump's heating output equals the building's heat loss. If a heat pump produces 30,000 BTU/hr at 47°F outdoor temperature and the building's heat loss is 30,000 BTU/hr at 20°F outdoor temperature, the balance point can be estimated graphically by plotting heat pump output (which decreases as outdoor temperature drops) against building heat loss (which increases as outdoor temperature drops). The intersection is the balance point. Below this temperature, auxiliary heat (electric resistance strips) activates. Modern cold-climate heat pumps can maintain their rated output to 0°F or below, significantly reducing auxiliary heat use.
Chapter 19: Air Conditioning
Exercise 19.1: SEER to Operating Cost Answer: Formula: Annual cooling cost = (Cooling load in BTU/yr) ÷ SEER × ($/kWh ÷ 1,000)
Example: A home with a 24,000 BTU (2-ton) AC system, running approximately 1,000 equivalent full-load hours per year:
- Annual BTU output = 24,000 BTU/hr × 1,000 hours = 24,000,000 BTU
- 13 SEER unit: 24,000,000 ÷ 13,000 = 1,846 kWh × $0.13 = **$240/year**
- 20 SEER unit: 24,000,000 ÷ 20,000 = 1,200 kWh × $0.13 = **$156/year**
- Annual savings from higher efficiency: $84/year
- Added cost of 20 SEER vs. 13 SEER unit: approximately $700–$1,200
- Simple payback: $950 ÷ $84 = 11.3 years
In hotter climates with longer cooling seasons (more equivalent full-load hours), payback shortens considerably. At 2,000 equivalent hours per year (common in Texas, Florida): savings double to $168/year, payback = 5.7 years.
Chapter 23: HVAC Efficiency Ratings
Exercise 23.1: AFUE vs. Heat Pump Heating Cost Answer: Comparing a 96% AFUE gas furnace to a heat pump with COP 3.0 for space heating:
Assumptions: 80 million BTU annual heating load; natural gas $1.20/therm; electricity $0.13/kWh (1 kWh = 3,412 BTU).
- 96% AFUE furnace: 80,000,000 ÷ 0.96 = 83.3 million BTU input; in therms: 83.3 million ÷ 100,000 = 833 therms × $1.20 = **$1,000/year**
- Heat pump (COP 3.0): 80,000,000 ÷ 3.0 = 26.7 million BTU electrical input; in kWh: 26,700,000 ÷ 3,412 = 7,826 kWh × $0.13 = **$1,017/year**
At these prices, the 96% gas furnace and a COP-3.0 heat pump cost approximately the same to operate. The heat pump becomes clearly cheaper when: electricity rates are lower, gas prices are higher, the heat pump achieves COP > 3.0 (modern cold-climate heat pumps often achieve 3.0–4.0), or a time-of-use electricity rate allows off-peak charging. The gas furnace becomes cheaper when: gas rates are below approximately $0.80/therm, the heat pump frequently operates below its balance point requiring expensive electric resistance backup.
Exercise 23.2: Break-Even Analysis for HVAC Replacement Answer: Scenario: Your 15-year-old, 10 SEER air conditioner needs a $900 repair (compressor capacitor and refrigerant charge). A new 18 SEER system costs $5,500 installed.
Net cost of replacing rather than repairing: $5,500 - $900 = $4,600 net additional investment in new equipment.
Annual operating savings (using Exercise 19.1 methodology for a 3-ton, 1,200 cooling hour application): - 10 SEER: (36,000 × 1,200) ÷ 10,000 × $0.13 = 4,320 kWh × $0.13 = $562/year - 18 SEER: (36,000 × 1,200) ÷ 18,000 × $0.13 = 2,400 kWh × $0.13 = $312/year - Annual savings: $250/year
Simple payback on replacement vs. repair: $4,600 ÷ $250 = 18.4 years
This suggests repair is the right choice if the system has 3–5 more years of life. But if the system is likely to fail completely within 2–3 years, the calculation changes: avoiding one emergency replacement (weekend service call premium, possible temporary rental equipment, hotel during a heat wave) can easily add $500–$1,000 to the cost of waiting.
The correct answer is not a single number — it is a decision framework that weighs remaining equipment life, repair cost trajectory, current efficiency, available rebates, and your personal financial situation.
Chapter 24: Roofing
Exercise 24.2: Estimating Roof Area Answer: For a gable roof, first calculate the footprint (length × width from ground). Then account for pitch. Roof pitch is expressed as rise over run (e.g., 6/12 means 6 inches of rise per 12 inches of run). The slope multiplier converts footprint area to actual roof area:
| Pitch | Slope Multiplier |
|---|---|
| 4/12 | 1.054 |
| 6/12 | 1.118 |
| 8/12 | 1.202 |
| 12/12 | 1.414 |
For a 40 × 30 foot footprint house with a 6/12 pitch: - Footprint area: 40 × 30 = 1,200 sq ft - Roof area: 1,200 × 1.118 = 1,342 sq ft of actual roof surface - In "squares" (roofing unit = 100 sq ft): 13.4 squares - Add 10–15% for waste and overlaps at edges: approximately 14.7–15.4 squares of materials needed.
Chapter 34: Hazardous Materials
Exercise 34.1: Radon Test Interpretation Answer: Interpreting a short-term radon test result:
- Result below 2.0 pCi/L: Low risk; no action required. Test again in 2–5 years.
- Result 2.0–3.9 pCi/L: Moderate. Consider mitigation, especially if you spend significant time in the basement. Follow up with a long-term test to confirm.
- Result 4.0 pCi/L or above: EPA recommends mitigation. A sub-slab depressurization (ASD) system typically reduces levels by 50–99% and costs $800–$2,500 to install. After installation, retest to confirm reduction.
- Result above 8 pCi/L: High priority; act promptly.
Note: A single short-term test (48–96 hours) can vary by 20–40% from long-term average due to weather, barometric pressure, and seasonal variation. If a short-term test is near 4 pCi/L, confirm with a long-term test (90+ days) before deciding on mitigation.
Chapter 39: Home Inspections
Exercise 39.1: Prioritizing Inspection Findings Answer (framework): Sort inspection findings into three categories:
Immediate/Safety: Electrical hazards (ungrounded wiring at GFCI-required locations, double-tapped breakers on full-capacity panels, exposed wiring), active gas leaks (confirmed by smell or testing), structural compromise (cracked or bowing foundation wall, cut load-bearing members), active water intrusion into electrical panels, inoperable smoke or CO detectors. These are non-negotiable; require professional remediation before occupancy or purchase.
Material defects with financial impact: Roof at or near end of life, failing HVAC equipment, evidence of sewer line problems (multiple slow drains, evidence of backflow), major drainage issues, significant moisture damage or evidence of active leaks. These warrant repair credit negotiation or may affect purchase price.
Maintenance items: Minor caulking failures, surface cracks in concrete flatwork, worn weather-stripping, aged but functional appliances, minor gutter issues. These are expected in any home with normal service life and are generally the buyer's responsibility to budget for.
The error most buyers make is treating everything on a 30-page inspection report as equally weighted. Focus negotiating capital on the top tier, and budget for the bottom tier as normal home maintenance.
For additional exercises not covered here, review the specific chapter's Key Takeaways section for the principles underlying the exercise. Most quantitative exercises in this book follow one of the frameworks above: energy-cost-payback calculations, load sizing calculations, or diagnostic interpretation frameworks. Mastering these patterns makes new calculations straightforward.