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Dwight and Mose decide to build a new barn on their farm,

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Dwight and Mose decide to build a new barn on their farm,

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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

OA D

Source: Veritas Prep

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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

OA D

Source: Veritas Prep
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

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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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