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

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Math Expert
Joined: 02 Sep 2009
Posts: 52902
Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

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21 Mar 2017, 03:59
1
14
00:00

Difficulty:

55% (hard)

Question Stats:

68% (03:12) correct 32% (03:18) wrong based on 224 sessions

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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

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Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

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12 Apr 2017, 12:57
6
quantumliner wrote:
Dwight = First Shift

Remaining Work = Total Work (Let us represent the total work as 1) = 1

Diwght completes 1/4th of the remaining work

Remaining Work = 1 - 1/4 = 3/4

Mose = First Shift

Remaining Work = 3/4

Mose completes 1/6th of the remaining work = 3/4 * 1/6 = 1/8

Remaining work = 3/4 - 1/8 = 5/8

Dwight = Second Shift

Remaining Work = 5/8

Diwght completes 1/4th of the remaining work = 5/8 * 1/4 = 5/32

Remaining work = 5/8 - 5/32 = 15/32

Mose = Second Shift

Remaining Work = 15/32

Mose completes 1/6th of the remaining work = 15/32 * 1/6 = 5/64

Remaining work = 15/32 - 5/64 = 25/64

Dwight = Third Shift

Remaining Work = 25/64

Diwght completes 1/4th of the remaining work = 25/64 * 1/4 = 25/256

Remaining work = 25/64 - 25/256 = 75/256

Work on the barn that is left to finish when Mose begins his third shift = 75/256

I'm not sure if I could do this in, lets say, 90 seconds...

Work remained
D1 (1-1/4)
M1 (1-1/4) - (1-1/4)x1/6 = (1-1/4)(1-1/6) = (3/4)(5/6) then:
D2 (3/4)(5/6)(3/4)
M2 (3/4)(5/6)(3/4)(5/6)
D3 (3/4)(5/6)(3/4)(5/6)(3/4) = 75/256

##### General Discussion
Senior Manager
Joined: 24 Apr 2016
Posts: 331
Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

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21 Mar 2017, 10:52
2
1
Dwight = First Shift

Remaining Work = Total Work (Let us represent the total work as 1) = 1

Diwght completes 1/4th of the remaining work

Remaining Work = 1 - 1/4 = 3/4

Mose = First Shift

Remaining Work = 3/4

Mose completes 1/6th of the remaining work = 3/4 * 1/6 = 1/8

Remaining work = 3/4 - 1/8 = 5/8

Dwight = Second Shift

Remaining Work = 5/8

Diwght completes 1/4th of the remaining work = 5/8 * 1/4 = 5/32

Remaining work = 5/8 - 5/32 = 15/32

Mose = Second Shift

Remaining Work = 15/32

Mose completes 1/6th of the remaining work = 15/32 * 1/6 = 5/64

Remaining work = 15/32 - 5/64 = 25/64

Dwight = Third Shift

Remaining Work = 25/64

Diwght completes 1/4th of the remaining work = 25/64 * 1/4 = 25/256

Remaining work = 25/64 - 25/256 = 75/256

Work on the barn that is left to finish when Mose begins his third shift = 75/256

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Joined: 20 Dec 2013
Posts: 121
Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

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12 Apr 2017, 13:25
2
1
Bunuel 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

Let total work be 256 units
Work remaining at the 5th shift (because Mose's third shift will be the sixth shift) = (256) *(3/4)*(5/6)*(3/4)*(5/6)*(3/4) = 75

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Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

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12 Apr 2017, 13:30
This seems like it would take too long

Posted from my mobile device
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Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

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12 Apr 2017, 13:31
gmathopeful19 wrote:
This seems like it would take too long

Posted from my mobile device

It wouldn't if you assume the work to be of 256 units.
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Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

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16 Jun 2017, 17:46
Why do you have to multiply the remaining amount of work by the amount being completed (as opposed to subtract)?
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Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

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16 Jun 2017, 20:53
This is something that we have to keep dividing by 4 and 6 (since 3/4 work is left, and 5/6 work is left), so better take a number which has atleast three 4's and three 6's. So lets take the initial barn work to be 4^3 * 6^3.

First shift:
Dwight does = 1/4 and work remaining = 3/4 * 4^3 * 6^3 = 3 * 4^2 * 6^3
Then Mose does = 1/6 and work remaining = 5/6 * 3 * 4^2 * 6^3 = 3 * 5 * 4^2 * 6^2

Second shift
Dwight does= 1/4 and remaining = 3/4 * 3 * 5 * 4^2 * 6^2 = 3^2 * 4 * 5 * 6^2
Mose does = 1/6 and work remaining = 5/6 * 3^2 * 4 * 5 * 6^2 = 3^2 * 5^2 * 4 * 6

Third Shift
Dwight does = 1/4 and work remaining for Mose = 3/4 * 3^2 * 5^2 * 4 * 6 = 3^3 * 5^2 * 6

So the fraction of work left = (3^3 * 5^2 * 6)/(4^3 * 6^3) = (27*25)/(64*36) = 75/256

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Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

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12 Dec 2017, 22:35
3
Let the work to be completed be 1.
D completes 1/4 of the remaining work. Therefore work remaining is $$(1-1/4)$$.
M completes 1/6 of the remaining work. Hence $$[(1-1/4)-(1-1/4)(1/6)]$$. Therefore work remaining is $$(1-1/4)(1-1/6)$$.

Hence work remaining when M starts work 3rd time is $$(1-1/4)^3*(1-1/6)^2 = 75/256$$
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Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

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17 Dec 2017, 02:39
PerfectScores wrote:
gmathopeful19 wrote:
This seems like it would take too long

Posted from my mobile device

It wouldn't if you assume the work to be of 256 units.

Can you explain why we assume the work to be of 256 units please?
Thank a lot.
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Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

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17 Dec 2017, 05:08
khiemchii wrote:
PerfectScores wrote:
gmathopeful19 wrote:
This seems like it would take too long

Posted from my mobile device

It wouldn't if you assume the work to be of 256 units.

Can you explain why we assume the work to be of 256 units please?
Thank a lot.

Hi,
Lets say total work is 256 .

D does 1/4 and M does 1/ of the remaining Unit .

Ist Attempt:

D = 1/4*256 = 64 , M = (256-64)*1/6 = 32

2nd Attempt:

D = (256 - 96)*1/4 = 40 , M = (256 - 136) *1/6= 20

3rd Attempt:

D = (256-156)*1/4= 25

At this point work remaining for M is 75 out of 256 . Hence 75/256 is answer
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Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

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31 Jan 2019, 17:49
Bunuel 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

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.

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Re: Dwight and Mose decide to build a new barn on their farm, and they beg  [#permalink]

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31 Jan 2019, 18:39
leandrodijon wrote:
quantumliner wrote:
Dwight = First Shift

Remaining Work = Total Work (Let us represent the total work as 1) = 1

Diwght completes 1/4th of the remaining work

Remaining Work = 1 - 1/4 = 3/4

Mose = First Shift

Remaining Work = 3/4

Mose completes 1/6th of the remaining work = 3/4 * 1/6 = 1/8

Remaining work = 3/4 - 1/8 = 5/8

Dwight = Second Shift

Remaining Work = 5/8

Diwght completes 1/4th of the remaining work = 5/8 * 1/4 = 5/32

Remaining work = 5/8 - 5/32 = 15/32

Mose = Second Shift

Remaining Work = 15/32

Mose completes 1/6th of the remaining work = 15/32 * 1/6 = 5/64

Remaining work = 15/32 - 5/64 = 25/64

Dwight = Third Shift

Remaining Work = 25/64

Diwght completes 1/4th of the remaining work = 25/64 * 1/4 = 25/256

Remaining work = 25/64 - 25/256 = 75/256

Work on the barn that is left to finish when Mose begins his third shift = 75/256

I'm not sure if I could do this in, lets say, 90 seconds...

Work remained
D1 (1-1/4)
M1 (1-1/4) - (1-1/4)x1/6 = (1-1/4)(1-1/6) = (3/4)(5/6) then:
D2 (3/4)(5/6)(3/4)
M2 (3/4)(5/6)(3/4)(5/6)
D3 (3/4)(5/6)(3/4)(5/6)(3/4) = 75/256

I dont understand this pattern. Could you please clarify how you got to your solution step by step?
Re: Dwight and Mose decide to build a new barn on their farm, and they beg   [#permalink] 31 Jan 2019, 18:39
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