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# Three machines, A, B, and C, can complete a certain task in 10 hours,

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Joined: 02 Sep 2009
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Three machines, A, B, and C, can complete a certain task in 10 hours,  [#permalink]

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04 Apr 2017, 04:51
1
5
00:00

Difficulty:

15% (low)

Question Stats:

87% (01:54) correct 13% (02:25) wrong based on 109 sessions

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Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job?

A. 4/5
B. 9/4
C. 11/4
D. 4
E. 13/2

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Re: Three machines, A, B, and C, can complete a certain task in 10 hours,  [#permalink]

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04 Apr 2017, 07:34
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1
In one hour three machines can complete (1/10 + 1/4 + 1/5) = 11/20 of the work

Work remaining = 9/20

(1/5)*x = 9/20
x = 9/4

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Joined: 04 Apr 2017
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04 Apr 2017, 08:21
The first machine(A) completed 10% ( 1/10 meaning 10 hours is 100% completion so 1 hour is 10% of it.

The second machine (B) completed 25% (1/4 meaning 4 hours is 100% completion so 1 hour is 25% completion )

The third machine (C) completed 20% (1/5)

Therefore, total completion is 10% + 25% + 20% = 55%
Percentage left for completion is 45% to be done by machine C
We can now use proportion.

100% ---- 5 hours
45% ---- X hours

Where X means unknown. )
(Consequently, we cross multiple the above)
100X = 45x5

100X = 225

X = 225/100 X = 9/4 or 2.25 or. 2 1/4

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Re: Three machines, A, B, and C, can complete a certain task in 10 hours,  [#permalink]

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02 Mar 2018, 10:42
Bunuel wrote:
Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job?

A. 4/5
B. 9/4
C. 11/4
D. 4
E. 13/2

The combined rate of A, B, and C is:

1/10 + 1/4 + 1/5 = 2/20 + 5/20 + 4/20 = 11/20. So if all the machines work for 1 hour, 11/20 of the job is completed, and 9/20 is left to be completed.

Thus, it would take machine C (9/20)/(1/5) = 45/20 = 9/4 hours to complete the job.

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Re: Three machines, A, B, and C, can complete a certain task in 10 hours,  [#permalink]

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22 Mar 2019, 11:24
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Re: Three machines, A, B, and C, can complete a certain task in 10 hours,   [#permalink] 22 Mar 2019, 11:24
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