A contractor needs to calculate the permissible exposure limit (PEL) for lead over an 8-hour workday. If air sampling shows 45 μg/m³ for 6 hours and 60 μg/m³ for 2 hours, what is the 8-hour time-weighted average?
Correct Answer
D) 48.75 μg/m³
TWA = [(45 × 6) + (60 × 2)] ÷ 8 = [270 + 120] ÷ 8 = 390 ÷ 8 = 48.75 μg/m³
Why This Is the Correct Answer
The 8-hour TWA is calculated using the formula: TWA = [(concentration₁ × time₁) + (concentration₂ × time₂)] ÷ total hours. Substituting: [(45 × 6) + (60 × 2)] ÷ 8 = [270 + 120] ÷ 8 = 390 ÷ 8 = 48.75 μg/m³. The Cal/OSHA PEL for lead is 50 μg/m³ as an 8-hour TWA. This result (48.75) is just below the PEL, meaning the Action Level (30 μg/m³) is still exceeded, which has its own compliance obligations.
Why the Other Options Are Wrong
Option A: 47.5 μg/m³
47.5 μg/m³ results from a simple average of the two concentrations: (45 + 60) ÷ 2 = 52.5, or could be from incorrectly weighting: (45 + 60) × 6/8 ≈ different wrong path. The simple average ignores the different time durations at each concentration level, which is the fundamental error the TWA formula corrects.
Option B: 55 μg/m³
55 μg/m³ is the arithmetic mean of 45 and 60 without time weighting — (45 + 60) ÷ 2 = 52.5, not 55 — or could reflect treating the 2-hour period as equal weight to the 6-hour period. Any method that ignores the unequal time periods will produce the wrong answer.
Option C: 52.5 μg/m³
52.5 μg/m³ is exactly the simple average of the two concentrations: (45 + 60) ÷ 2 = 52.5. This is the most common wrong answer because it uses the correct values but applies simple averaging instead of time-weighted averaging. In a TWA, more time at a lower concentration should pull the result lower than the arithmetic mean.
Memory Technique
TWA = Total Weighted Amount ÷ Total Hours. Calculate the total weighted amount first: multiply each concentration by its hours, add them together. Then divide by 8 (the full workday). It is a weighted average, not a simple average.
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