Two mowers and one field

Question

Adam can mow a field in 1 hour. Bob is faster: in the same hour he can mow 2 fields. Working together, how long do they take to mow one field? Give the general rule for combining two workers' times, and explain why simply averaging their times gives the wrong answer.

Accepted Answer

20 minutes. Rates. Adam mows 1 field per hour. Bob mows 2 fields per hour. Together they mow 3 fields per hour. Time for one field. At 3 fields per hour, one field takes 1/3 of an hour, which is 20 minutes. The common mistake. People average the times (Adam's 60 minutes and Bob's 30 minutes give 45) or halve something. But when two people work simultaneously, what adds is the amount of work done per minute, so you must add rates. The general formula for two workers who take times a and b alone is ab/(a + b) together: here 60 × 30 / 90 = 20 minutes. A check. In 20 minutes Adam does a third of …

Two mowers and one field

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