Calculate the maximum allowable lead exposure for an 8-hour workday under Cal/OSHA regulations. If a worker is exposed to 35 μg/m³ for 6 hours and 45 μg/m³ for 2 hours, what is the time-weighted average exposure?
Correct Answer
C) 37.5 μg/m³
TWA = [(35 × 6) + (45 × 2)] ÷ 8 = [210 + 90] ÷ 8 = 300 ÷ 8 = 37.5 μg/m³. This is below the Cal/OSHA PEL of 50 μg/m³.
Why This Is the Correct Answer
Time-Weighted Average (TWA) = [(concentration₁ × time₁) + (concentration₂ × time₂)] ÷ total hours = [(35 × 6) + (45 × 2)] ÷ 8 = [210 + 90] ÷ 8 = 300 ÷ 8 = 37.5 μg/m³. This is below the Cal/OSHA Permissible Exposure Limit (PEL) of 50 μg/m³ for lead.
Why the Other Options Are Wrong
Option A: 45.0 μg/m³
45.0 μg/m³ represents just the higher exposure period (45 μg/m³ for 2 hours) applied to the full shift — this ignores the 6-hour lower-exposure period entirely and does not follow TWA methodology.
Option B: 40.0 μg/m³
40.0 μg/m³ would be a simple arithmetic average of the two concentrations ((35 + 45) ÷ 2 = 40), which is incorrect because it ignores the different time durations for each exposure level.
Option D: 42.5 μg/m³
42.5 μg/m³ results from a common calculation error, such as incorrectly weighting the two time periods or making an arithmetic mistake. The correct weighted calculation yields 37.5, not 42.5.
Memory Technique
Think of TWA like a weighted GPA: each 'grade' (concentration) must be multiplied by its 'credit hours' (time) before averaging. Formula: TWA = Σ(C × T) ÷ 8. The total must always divide by 8 (or actual hours worked), not by the number of different exposure levels.
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