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John takes 5 hours to complete a job, Bill takes x hours to complete a

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Bunuel
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John takes 5 hours to complete a job, Bill takes x hours to complete a [#permalink] New post   30 Jun 2021, 02:15
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John takes 5 hours to complete a job, Bill takes x hours to complete a job, and together they take y hours to complete a job. If Bill is twice as fast as John in completing the job, what is y?

A. 5/4
B. 5/3
C. 5/2
D. 3
E. 3.5
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B
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Re: John takes 5 hours to complete a job, Bill takes x hours to complete a [#permalink] New post   30 Jun 2021, 02:42
b 5/3

IMO, we need ot work (Rj+Rb)*y=1, given Johns time Jt=5, work 1 Rj=1/5, if rate for Bil is twice that of John then Rb=2*(1/5) i.e. 2/5. with that we can fill in (Rj+Rb) ---->3/5 therefore (Rj+Rb)*y=1 ---> (3/5)y=1, y=5/3
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Re: John takes 5 hours to complete a job, Bill takes x hours to complete a [#permalink] New post   30 Jun 2021, 03:50
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Solution:

It is given that John takes \(5\) hours to complete a job. So the rate of working for John \(= \frac{1}{5}\).

Bill takes \(x\) hours to complete a job. So the rate of working for Bill \(= \frac{1}{x}\).

Together they take y hours to complete a job. So, we can write: \(\frac{1}{5} + \frac{1}{x} = \frac{1}{y}\)

It is given that Bill is twice as fast as John which means \(x = 2.5\) hours

So, \(\frac{1}{5} + \frac{1}{x} = \frac{1}{y}\)

⇒ \(\frac{1}{5} + \frac{1}{2.5} = \frac{1}{y}\)

⇒ \(\frac{5+10}{25} = \frac{1}{y}\)

⇒ \(y = 5/3\)

Hence the right answer is Option B.
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Re: John takes 5 hours to complete a job, Bill takes x hours to complete a [#permalink] New post   30 Jun 2021, 08:10
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Since Bill is twice as fast as John, rate of Bill = 2 * rate of John. Therefore, time taken by Bill = ½ * time taken by John.

Since John takes 5 hours to complete the job, Bill would take \(\frac{5}{2}\) hours to complete the job.

Let the job = LCM (5, 5/2) = 5 units.

Rate of John = 1 unit per hour; rate of Bill = 2 units per hour.
Combined rate of John & Bill = 3 units per hour.

Time taken to complete the job of 5 units = y = \(\frac{5}{3}\) hours

The correct answer option is B.

Hope that helps!
Aravind B T
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Re: John takes 5 hours to complete a job, Bill takes x hours to complete a [#permalink]
30 Jun 2021, 08:10
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