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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?

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

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This post received KUDOS

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

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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07 Jan 2016, 02:57

My answer is C. 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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Never forget what you are fighting for... and when your mind and your body tell you to quit. Your heart will tell you to fight.

Last edited by Kingsman on 21 Jan 2016, 17:56, edited 1 time in total.

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.

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.

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

Answer: C
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