ardz24 wrote: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?
A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours
E. 7 hours
Let the driveway = the LCM of 6 and 8 = 24 units.
Since Mary can pave the 24-unit driveway in 8 hours, Mary's rate alone = w/t = 24/8 = 3 units per hour.
Since Hilary can pave the 24-unit driveway in 6 hours, Hilary's rate alone = w/t = 24/6 = 4 units per hour.
Working together:
Mary's rate increased by 1/3 = 3 + (1/3)(3) = 4 units per hour.
Hilary's rate decreased by 50% = 4 - (1/2)(4) = 2 units per hour.
Combined rate for Mary and Hilary = 4+2 = 6 units per hour.
Since their combined rate is 6 units per hour, the time for Mary and Hilary to pave the 24-unit driveway = w/r = 24/6 = 4 hours.
The correct answer is
B.
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