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# Working at a constant rate, Sam can finish a job in 3 hours. Mark, als

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Math Expert
Joined: 02 Sep 2009
Posts: 46035
Working at a constant rate, Sam can finish a job in 3 hours. Mark, als [#permalink]

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03 Jan 2016, 12:46
4
1
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:23) correct 29% (01:45) wrong based on 197 sessions

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Working at a constant rate, Sam can finish a job in 3 hours. Mark, also working at a constant rate, can finish the same job in 12 hours. If they work together for 2 hours, how many minutes will it take Sam to finish the job, working alone at his constant rate?

A. 5
B. 20
C. 30
D. 60
E. 120

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Joined: 20 Feb 2015
Posts: 386
Concentration: Strategy, General Management
Re: Working at a constant rate, Sam can finish a job in 3 hours. Mark, als [#permalink]

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06 Jan 2016, 02:53
2
in an hour sam can do 1/3 and for mark it is 1/12
sam's efficiency =100/3=33.33
mark's efficiency = 100/12=8.33
in two hours they completed = 83.32% of the work
work remaining = 16.68 %
time take by sam in minutes = (16.68/33.33)*60 =30.027 = ~30 minutes
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Joined: 20 Aug 2015
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Location: India
GMAT 1: 760 Q50 V44
Re: Working at a constant rate, Sam can finish a job in 3 hours. Mark, als [#permalink]

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07 Jan 2016, 02:26
1
1
Bunuel wrote:
Working at a constant rate, Sam can finish a job in 3 hours. Mark, also working at a constant rate, can finish the same job in 12 hours. If they work together for 2 hours, how many minutes will it take Sam to finish the job, working alone at his constant rate?

A. 5
B. 20
C. 30
D. 60
E. 120

Always assume the total work to be the LCM of the time given. This makes the calculations easier.

Assume the total work = 12 units.
Sam's rate of work = 12/3 = 4 units/hour
Mark's rate of work = 12/12 = 1 units/hour

Work completed by Sam and Mark together in 2 hours = 2(4 + 1) = 10 units.

Remaining work = 2 units.
Time taken by Sam in minutes = 2/4*60 = 30 minutes
Option C
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Working at a constant rate, Sam can finish a job in 3 hours. Mark, als [#permalink]

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Updated on: 21 Jan 2016, 17:56
Sol: Work = Rate x Hour
We have this table:
Hour-----Rate-----Work
Sam 3 1/3 1
Mark 12 1/12 1

They work together for 2 hours then the amount of work finished: 2*(1/3 + 1/12) = 5/6
The work remaining for Sam to finish: 1 - 5/6 =1/6
Hours need for Sam to finish: 1/6 : 1/3 = 1/2 hour = 30 mins
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Originally posted by Kingsman on 07 Jan 2016, 02:57.
Last edited by Kingsman on 21 Jan 2016, 17:56, edited 1 time in total.
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Working at a constant rate, Sam can finish a job in 3 hours. Mark, als [#permalink]

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21 Jan 2016, 13:59
CounterSniper wrote:
in an hour sam can do 1/3 and for mark it is 1/12
sam's efficiency =100/3=33.33
mark's efficiency = 100/12=8.33
in two hours they completed = 83.32% of the work
work remaining = 16.68 %
time take by sam in minutes = (16.68/33.33)*60 =30.027 = ~30 minutes

I have never used this method but looks very interesting (like a jolly you can use in difficult situations)!!!

Is there a name for it?

I used this method anyway:
Sam can do 1/3 of the job in 1 hour. Mark 1/12 in one hour.
They work together 2 hours so = 1/3*2 + 1/12*2= 5/6. This is the amount of work the have already done.
Now to estimate how many minutes left to Sam, we can simply subtract the rate of Sam to what is done by Sam and Mark, which is = 1/3 - 5/6 = 1/2. So Sam left with 1/2 of hour = 30 mins.
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Joined: 22 May 2016
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Working at a constant rate, Sam can finish a job in 3 hours. Mark, als [#permalink]

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27 Sep 2017, 10:53
Bunuel wrote:
Working at a constant rate, Sam can finish a job in 3 hours. Mark, also working at a constant rate, can finish the same job in 12 hours. If they work together for 2 hours, how many minutes will it take Sam to finish the job, working alone at his constant rate?

A. 5
B. 20
C. 30
D. 60
E. 120

Standard $$rt = W$$ works well here

Sam's rate = $$\frac{1}{3}$$

Mark's rate = $$\frac{1}{12}$$

1) Rate at which they work together:

$$(\frac{1}{3}$$ + $$\frac{1}{12})$$ = $$\frac{15}{36}$$ = $$\frac{5}{12}$$ is combined rate

2) In two hours, they finish how much work? $$W = rt$$

W = $$(\frac{5}{12} * 2) = \frac{5}{6}$$ of work is finished

3) Time, in minutes, for Sam to finish remaining work alone? (Work/Sam's rate) = Sam's time. Then convert hours to minutes.

$$\frac{1}{6}$$ of work remains

$$\frac{\frac{1}{6}}{\frac{1}{3}} =(\frac{1}{6} * 3) =\frac{1}{2}hr$$

$$\frac{1}{2}hr$$ = $$30$$ minutes*

*$$\frac{1}{2}hr$$ = 30 minutes is easy. With harder numbers, just multiply any fraction of an hour by 60 to get minutes. Example:

$$(\frac{17}{12}hr)$$ * (60) = 85 minutes

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Re: Working at a constant rate, Sam can finish a job in 3 hours. Mark, als [#permalink]

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01 Oct 2017, 12:13
Bunuel wrote:
Working at a constant rate, Sam can finish a job in 3 hours. Mark, also working at a constant rate, can finish the same job in 12 hours. If they work together for 2 hours, how many minutes will it take Sam to finish the job, working alone at his constant rate?

A. 5
B. 20
C. 30
D. 60
E. 120

The rate of Sam is 1/3 and the rate of Mark is 1/12. We can let Sam’s time = 2 + x hours and Mark’s time = 2 hours; thus:

(1/3)(2 + x) + (1/12)(2) = 1

(2 + x)/3 + 1/6 = 1

Multiplying the equation by 6, we have:

4 + 2x + 1 = 6

2x = 1

x = 1/2 hour = 30 minutes

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Re: Working at a constant rate, Sam can finish a job in 3 hours. Mark, als   [#permalink] 01 Oct 2017, 12:13
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