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B can work 3 times faster than A. They work together on a task and complete it in a day. How long does it take for B alone to complete the task?

Correct answer: A. 32 hours

  • A. 32 hours
  • B. 48 hours
  • C. 3 days
  • D. 4 days

Explanation

If A works at x work per day, B works at 3x work per day, so together they work at 4x = 1 work per day. Thus B's rate is 3/4 work per day, giving B a time of 1 ÷ 3/4 = 4/3 days = 32 hours. The likely mistake is choosing 48 hours by treating B's rate as half the combined rate instead of three-fourths.

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About Time and Work

Problems measure work through rates, treating each person's or machine's contribution as work completed per unit time. Questions cover combined work, efficiency, wages, alternate working schedules, pipes and cisterns, and men-days relationships, with care needed to distinguish time taken by one worker from the time required when workers act together.

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