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Sam can complete a certain task in 4 hours while Peter needs only 3 ho

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Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]

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New post 09 Jan 2018, 23:46
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Question Stats:

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Sam can complete a certain task in 4 hours while Peter needs only 3 hours to complete the same task. If Sam starts working on the task and half an hour later Peter joins him, how many hours will it take them to complete the task together?

A. 3/2
B. 12/7
C. 2
D. 31/14
E. 5/2

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Re: Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]

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New post 10 Jan 2018, 02:40
Peter works at 4/3 of Sam's speed, so together at 1 + 4/3 = 7/3 times Sam's speed. When Peter joins, Sam would have 7/2 hours left on his own. So together: 3/7 * 7/2 = 3/2 hours.

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Re: Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]

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New post 10 Jan 2018, 03:22
Bunuel wrote:
Sam can complete a certain task in 4 hours while Peter needs only 3 hours to complete the same task. If Sam starts working on the task and half an hour later Peter joins him, how many hours will it take them to complete the task together?

A. 3/2
B. 12/7
C. 2
D. 31/14
E. 5/2


As the calculation looks straightforward, we'll just do it.
This is a Precise approach.

Sam works at a rate of T/4 and Peter at a rate of T/3.
Together they work at a rate of T/4+T/3 = 7T/12.
In half an hour Sam completes T/8 units of work so we can write:
7T/12 * hours = T - T/8 = 7T/8.
Simplifying gives 12/8 = 3/2 hours, answer (A).
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Re: Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]

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New post 10 Jan 2018, 08:50
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Bunuel wrote:
Sam can complete a certain task in 4 hours while Peter needs only 3 hours to complete the same task. If Sam starts working on the task and half an hour later Peter joins him, how many hours will it take them to complete the task together?

A. 3/2
B. 12/7
C. 2
D. 31/14
E. 5/2

Let the total work be 24 units

Efficiency of Sam is 6 units/hour
Efficiency of Peter is 8 units/hour

Work completed by Sam in half hour is 3 units, work left is 21 units

Combined efficiency of Sam and Peter is 14 units, so time required to complete the remaining piece of work is \(\frac{21}{14}\) = \(\frac{3}{2}\) Hours

Answer will be (A)
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Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]

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New post 10 Jan 2018, 12:38
Bunuel wrote:
Sam can complete a certain task in 4 hours while Peter needs only 3 hours to complete the same task. If Sam starts working on the task and half an hour later Peter joins him, how many hours will it take them to complete the task together?

A. 3/2
B. 12/7
C. 2
D. 31/14
E. 5/2

Rates:
Sam's rate: \(\frac{1}{4}\)
Peter's rate: \(\frac{1}{3}\)
Combined rate: \(\frac{1}{4} +
\frac{1}{3}=\frac{7}{12}\)

First part of work:
Sam alone for \(\frac{1}{2}\) hour. R*T = W
\(\frac{1}{4} * \frac{1}{2} =\frac{1}{8}\) W finished
\(\frac{7}{8}\) of work remains for both to finish

Second part of work, W/R = T
\(\frac{\frac{7}{8}}{\frac{7}{12}} =(\frac{7}{8} * \frac{12}{7}) = \frac{12}{8}=\frac{3}{2}\)

Answer A
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Sam can complete a certain task in 4 hours while Peter needs only 3 ho [#permalink]

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New post 16 Jan 2018, 17:46
Bunuel wrote:
Sam can complete a certain task in 4 hours while Peter needs only 3 hours to complete the same task. If Sam starts working on the task and half an hour later Peter joins him, how many hours will it take them to complete the task together?

A. 3/2
B. 12/7
C. 2
D. 31/14
E. 5/2


We can let Sam’s rate = 1/4, and Peter’s rate = 1/3.

We can let the time Sam worked = 1/2 + x and the time Peter worked = x

Thus:

1/4(1/2 + x) + 1/3(x) = 1

1/8 + x/4 + x/3 = 1

Multiplying the entire equation by 24, we have:

3 + 6x + 8x = 24

14x = 21

x = 21/14 = 3/2 hours

Answer: A
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Sam can complete a certain task in 4 hours while Peter needs only 3 ho   [#permalink] 16 Jan 2018, 17:46
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