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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BTGmoderatorAT 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?

The best way to solve this problem is to keep track of the fraction of the barn that still needs to be completed after each of their shifts:

Dwight's 1st shift: 1/4 ----Fraction of the barn still needs to be completed: 3/4

Mose's 1st shift: 1/6(3/4) = 1/8----Fraction of the barn still needs to be completed: 5/6(3/4) = 5/8

Dwight's 2nd shift: 1/4(5/8) = 5/32 ----Fraction of the barn still needs to be completed: 3/4(5/8) = 15/32

Mose's 2nd shift: 1/6(15/32) = 5/64 ----Fraction of the barn still needs to be completed: 5/6(15/32) = 25/64

Dwight's 3rd shift: 1/4(25/64) = 25/256 ----Fraction of the barn still needs to be completed: 3/4(25/64) = 75/256

We can see that before Mose begins his 3rd shift, 75/256 of the barn still needs to be completed.

Answer: D