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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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Math Expert
Joined: 02 Sep 2009
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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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07 May 2017, 12:47
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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
[Reveal] Spoiler: OA

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Posts: 333
Ali and Moe can do a certain job together in 4 hours and Ali is 5 time [#permalink]

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07 May 2017, 14:00
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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

Last edited by quantumliner on 07 May 2017, 19:48, edited 1 time in total.
Intern
Joined: 12 Nov 2016
Posts: 16
Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time [#permalink]

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07 May 2017, 15:20
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
Intern
Joined: 12 Nov 2016
Posts: 16
Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time [#permalink]

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07 May 2017, 15:30
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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

Intern
Joined: 26 Feb 2014
Posts: 7
GMAT 1: 700 Q49 V35
GPA: 4
Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time [#permalink]

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07 May 2017, 15:52
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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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Joined: 26 Feb 2016
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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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07 May 2017, 22:20
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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Joined: 07 Jul 2012
Posts: 275
Location: India
Concentration: Finance
Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time [#permalink]

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08 May 2017, 03:22
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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.

Kudos please if you like my explanation!
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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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08 May 2017, 06:37
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)
Re: Ali and Moe can do a certain job together in 4 hours and Ali is 5 time   [#permalink] 08 May 2017, 06:37
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