BTGmoderatorDC wrote:Dwight and Mose decide to build a new barn on their farm, and they begin to work in alternating shifts, with Dwight taking the first shift. During each of his shifts, Dwight does 1/4 of the remaining work. During each of his shifts, Mose does 1/6 of the remaining work. How much of the barn is left to finish when Mose begins his third shift?
A. 1/24
B. 5/36
C. 25/72
D. 75/256
E. 255/512
Every time Dwight does 1/4 of the remaining work, 3/4 of the work remains.
Every time Mose does 1/6 of the remaining work, 5/6 of the work remains.
When Mose starts his third shift, Dwight has completed 3 shifts, while Mose has completed 2 shifts.
Thus, the remaining work at the start of Mose's third shift = (3/4)(3/4)(3/4)(5/6)(5/6) = 75/256.
The correct answer is
D.
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