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Ali and Moe can do a certain job together in 4 hours and Ali is 5 time

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Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 07 May 2017, 13:47
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Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?

A. 3 hours 20 minutes
B. 4 hours 12 minutes
C. 4 hours and 48 minutes
D. 5 hours
E. 5 hours and 20 minutes

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Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post Updated on: 07 May 2017, 20:48
1
Rate at which Ali works = 1/a
Rate at which Moe works = 1/m

(1/a + 1/m) * 4 = 1

1/a = 5 * 1/m

(1/a + 1/5a) * 4 = 1

6*4/5a = 1

a = 24/5 hours = 4.8 hours = 4 hours 48 minutes

Answer is C. 4 hours 48 minutes

Originally posted by quantumliner on 07 May 2017, 15:00.
Last edited by quantumliner on 07 May 2017, 20:48, edited 1 time in total.
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 07 May 2017, 16:20
Let us assume the total work which needs to be done is 120 units (LCM of 4,5 and 6 which are basically the numbers used in the question).
Therefore, the work completed by Ali and Moe in 1 hour = 120 units/4 hours i.e. 30 units/hour.
Now, we know that Ali is 5 times faster than Moe. So, if the total work was 30 units/hour, Ali would finish 25 units and Moe, 5 units.
So, if Ali were to finish the task alone, he'll need to finish 120 units at a rate of 25 units/hour. i.e. 120 units/ 25 units = 4.8 which translates to 4 hours and 48 minutes.
Hence, option C is the correct answer.

Hope it helps :)
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 07 May 2017, 16:30
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1
quantumliner wrote:
Rate at which Ali works = 1/a
Rate at which Moe works = 1/m

(1/a + 1/m) * 4 = 1

1/a = 5 * 1/m

(1/a + 1/5a) * 4 = 1

6*4/5a = 1

a = 24/5 hours = 4.2 hours = 4 hours 12 minutes

Answer is B. 4 hours 12 minutes



Could you please help me with understanding your approach?
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 07 May 2017, 16:52
1
Let M's speed = s
A's speed = 5s
Combined speed = 6s, time taken to complete work = 4 hours.
Hence total work = speed * time = 6s * 4 = 24s
Now, if only A does the work, then time taken = total work/speed of A = 24s/5s = 24/5 hours = 4 hours 48 mins.
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 07 May 2017, 23:20
Total work : 120 units
Both can do the work in 4 hours(Rate of combined work is 30 units/hr)
Let the rate of Moe be x, hence rate of Ali is 5x. Combined rate is 6x.
Equating the two, x=5units
Time taken by Moe alone to do the work is 24/5 = 4 hours 4/5*60 mins or 4 hours 48 minutes(Option C)

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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 08 May 2017, 04:22
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Let time taken by Ali = x hours
time taken by Moe= 5x hours

Work done by both of them in 1 hour:

\(\frac{1}{x}\) + \(\frac{1}{5x}\)= \(\frac{1}{4}\)

\(\frac{5 +1}{5x}\) =\(\frac{1}{4}\)

\(\frac{6}{5x}\)= \(\frac{1}{4}\); x= \(\frac{24}{5}\); x= 4\(\frac{4}{5}\) or 4 hour 48 mins

Thus, Time taken by Ali= 4 hours 48 mins.

Answer: C.

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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time  [#permalink]

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New post 08 May 2017, 07:37
Bunuel wrote:
Ali and Moe can do a certain job together in 4 hours and Ali is 5 times faster than Moe. If Ali does the job by himself, how long does it take him to complete the job working at the same rate?

A. 3 hours 20 minutes
B. 4 hours 12 minutes
C. 4 hours and 48 minutes
D. 5 hours
E. 5 hours and 20 minutes


Ali + Moe = \(\frac{1}{4}\) of a job an hour

Ali = 5 Moes (5M)

Ali + Moe = 6 Moes (6M)

Ali + Moe = 6M = \(\frac{1}{4}\) of a job an hour

1 Moe = \(\frac{1}{24}\) of a job an hour

Ali = 5 Moes = \(\frac{5}{24}\) of a job an hour

\(\frac{24}{5}\) = 4 \(\frac{4}{5}\) hours

4 \(\frac{4}{5}\) hours = 4.48 hours (C)
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Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time &nbs [#permalink] 08 May 2017, 07:37
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