Working alone, Mary can pave a driveway in 8 hours and Hilla

[BTGmoderatorAT]

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

Is there a strategic solution to this question? Can any experts help?

[GMATGuruNY]

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.

[Jeff@TargetTestPrep]

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

Mary's original rate = 1/8, and when she works with Hilary, her new rate is 1/8 x 1 1/3 = 1/8 x 4/3 = 4/24 = 1/6.

Hillary's original rate = 1/6, and when she works with Mary, her new rate is 1/6 x 1/2 = 1/12.

Thus, their combined new rate is 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4. This rate of 1/4 is interpreted as "1 driveway per 4 hours," so the time it takes them to complete the driveway is 4 hours.

Answer: B