A and B start working together on a certain task. A alone can complete it in…
2018
A and B start working together on a certain task. A alone can complete it in 40 hours, and B alone can complete it in 60 hours. If A leaves the work 10 hours before the task is actually completed, in how many hours will the work be completed?
Answer: D. 30 — When two people work on a task together — even if one of them stops before the task is finished — the fraction of the task each person completes equals their…
- A.
39
- B.
42
- C.
44
- D.
30
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Correct answer: D
When two people work on a task together — even if one of them stops before the task is finished — the fraction of the task each person completes equals their individual work rate (1 ÷ the time they would take alone) multiplied by the number of hours they actually work. The task is finished exactly when these fractions together add up to 1 (the whole task).
Let the total time taken to complete the task be T hours — this is the value being asked for.
A's work rate is 1/40 of the task per hour, and B's work rate is 1/60 of the task per hour.
A leaves 10 hours before the task is actually completed, so A works for (T − 10) hours, while B works the entire T hours.
The total-work equation is therefore (T − 10)/40 + T/60 = 1.
Multiplying throughout by 120 (the LCM of 40 and 60) clears the fractions: 3(T − 10) + 2T = 120.
Expanding and simplifying: 3T − 30 + 2T = 120, so 5T = 150, giving T = 30.
Cross-check: with T = 30, A works (30 − 10) = 20 hours, completing 20/40 = 1/2 of the task, and B works the full 30 hours, completing 30/60 = 1/2 of the task; the two halves together make up the whole task, confirming the total time is 30 hours.