M7MBA wrote:Jamshid can paint a fence in 50 percent less time than Taimour can when each works alone. When they work together, they can paint the fence in 8 hours. How long would it take Taimour to paint the fence alone?
(A) 6 hours
(B) 8 hours
(C) 14 hours
(D) 24 hours
(E) 32 hours
We can PLUG IN THE ANSWERS, which represent Taimour's time alone.
Since Jamshid and Taimour working together takes 8 hours to paint the fence, Taimour's time alone must be more than 8 hours.
Eliminate A and B.
When the correct answer is plugged in, Jamshid's time alone will be 50% less than Taimour's time alone.
In other words, Jamshid's time alone will be 1/2 Tamour's time alone.
D: Taimour's time alone = 24 hours
Let the fence = 24 units.
Since Taimour alone takes 24 hours to paint the 24-unit fence, Taimour's rate = w/t = 24/24 = 1 unit per hour.
Since Jamshid and Taimour together take 8 hours to paint the 24-unit fence, their combined rate = w/t = 24/8 = 3 units per hour.
Jamshid's rate = (combined rate for Jamshid and Taimour) - (Taimour's rate alone) = 3-1 = 2 units per hour.
Since Jamshid's rate = 2 units per hour, Jamshid's time alone to produce the 24-unit fence = w/r = 24/2 = 12 hours.
Success!
Jamshid's time alone (12 hours) is 1/2 Taimour's time alone (24 hours).
The correct answer is
D.
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