A alone can do a job in 4 hours; (B + C) together in 3 hours; (A + C) together in 2 hours. How long will B alone take?

Problem restatement
Given three composite times involving A, B, and C, find B's solo time.

Given data

• a = 1/4 job/hour.
• b + c = 1/3 job/hour.
• a + c = 1/2 job/hour.

Concept/Approach
Isolate c from (a + c), then subtract from (b + c) to get b.

Step-by-step calculation
c = (a + c) − a = 1/2 − 1/4 = 1/4 b = (b + c) − c = 1/3 − 1/4 = (4 − 3)/12 = 1/12 job/hour B's time = 1 ÷ (1/12) = 12 hours

Verification
Check consistency: a = 1/4, c = 1/4 → (a + c) = 1/2 (given). Then (b + c) = 1/12 + 1/4 = 1/3 (given).

Common pitfalls

• Adding or subtracting the times rather than the rates.

Final Answer
12 hours