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Working alone, Lia can mow a sports field in 3 hours, and working alone, Theo can mow the same field in 6 hours. If they work together at their individual constant rates, how many hours will it take them to mow the field?
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Correct answer
B
Add rates, not times. Lia's rate is 1/3 of the field per hour, and Theo's rate is 1/6 of the field per hour. Their combined rate is 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 of the field per hour.
The time to finish the field together is 1 ÷ (1/2) = 2 hours. Notice this result is less than either person's solo time, which is the sanity check for a working-together problem.
Averaging the times to get 4.5 or adding them to get 9 both ignore that Lia and Theo work at the same time, not one after the other.
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