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# If Kyle works alone, he can wash the night shift dishes in 55 minutes.

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Joined: 02 Sep 2009
Posts: 65828
If Kyle works alone, he can wash the night shift dishes in 55 minutes.  [#permalink]

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14 Jul 2020, 02:54
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Question Stats:

97% (01:54) correct 3% (03:33) wrong based on 38 sessions

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If Kyle works alone, he can wash the night shift dishes in 55 minutes. It will only take him 40 minutes if he works, together with Harry. How long will it take Harry to wash the night shift dishes by himself?

A. 65
B. 87
C. 95
D. 147
E. 165

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Re: If Kyle works alone, he can wash the night shift dishes in 55 minutes.  [#permalink]

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14 Jul 2020, 06:45
1
If Kyle works alone, he can wash the night shift dishes in 55 minutes. It will only take him 40 minutes if he works, together with Harry.
So,
Let Harry complete work in x minutes
And they do 1/55 & 1/x work in 1 minute
1/55 + 1/x = 1/40
(X+55)/55x = 1/40
40X+2200 = 55x
2200 = 15X
X = 146.666
Or X = 147

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Re: If Kyle works alone, he can wash the night shift dishes in 55 minutes.  [#permalink]

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14 Jul 2020, 10:02
Kyle's rate: 55 minutes
Rate of work together: 40 minutes
Harry's rate : h

using the combined rates formula :ab/ a+ b........ 55h/ 55+ h=40
solving for h, we get h=146.66

OA: D. 147
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Re: If Kyle works alone, he can wash the night shift dishes in 55 minutes.  [#permalink]

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14 Jul 2020, 15:31
Bunuel wrote:
If Kyle works alone, he can wash the night shift dishes in 55 minutes. It will only take him 40 minutes if he works, together with Harry. How long will it take Harry to wash the night shift dishes by himself?

A. 65
B. 87
C. 95
D. 147
E. 165

Notate K and H as their efficiencies.

Translating the information gives K = 1/55 and K + H = 1/40.

55 = 5*11 and 40 = 5*8, their LCM is 5 * 8 * 11.

H = 1/40 - 1/55 = $$\frac{11}{440} - \frac{8}{440}$$ = $$\frac{3}{440}$$.

However this is his efficiency, the amount of time needed is 1/H = 440/3 which is a little smaller than 150.

Ans: D
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Re: If Kyle works alone, he can wash the night shift dishes in 55 minutes.   [#permalink] 14 Jul 2020, 15:31

# If Kyle works alone, he can wash the night shift dishes in 55 minutes.

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