Question

Working alone, Mary can pave a driveway in 8 hours and Hillary can pave the same driveway in 6 hours. When they work together, Mary thrives on teamwork so her rate increases by 33.33%, but Hillary becomes distracted and her rate decreases by 50%. If they both work together, how many hours will it take to pave the driveway?

Answer 1

Answer:

Initial working rates:

Mary = 1/8 per hour

Hillary = 1/6 per hour

Rate when working together:

Mary = 1/8 + (1/3*1/8) = 3/24 + 1/24 = 4/24 = 1/6 per hour

Hillary = 1/6 - (1/2*1/6) = 2/12 - 1/12 = 1/12 per hour

Together they work 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4 per hour

So they will need 4 hours to complete the driveway.

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