ardz24 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
I'm confused how to set up the formulas here. Can any experts help?
Say the total work is 1.
Work done by Dwight in his first shift = 1/4th of 1 = 1/4;
Work remaining = 1 - 1/4 = 3/4;
Work done by Mose in his first shift = 1/6th of 3/4 = 1/8;
Work remaining = 3/4 - 1/8 = 5/8;
Work done by Dwight in his second shift = 1/4th of 5/8 = 5/32;
Work remaining = 5/8 - 5/32 = 15/32;
Work done by Mose in his second shift = 1/6th of 15/32 = 5/64;
Work remaining = 15/32 - 5/64 = 25/64;
Work done by Dwight in his third shift = 1/4th of 25/64 = 25/256;
Work remaining = 25/64 - 25/256 = 75/256 = work left to finish when Mose begins his third shift
The correct answer:
E
Hope this helps!
-Jay
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