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Work Problem - Logic or work formula

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by sal_xcool » Thu Feb 24, 2011 9:31 pm
If 5 machines can do 3 jobs in 7 hours, how long will it take 2 machines to do 5 jobs? Assume all jobs and
machines are equal.

A. 5 hours, 10 minutes
B. 11 hours, 40 minutes
C. 12 hours, 30 minutes
D. 18 hours, 40 minutes
E. 29 hours, 10 minutes

OA E

I always have problem with work problems.
I don't know what the best strategy is to tackle these problems. Using the work formula or logic.
When I look at this question, I have no clue how to use the work formula.
Any suggestion would be greatly appreciated.
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by Anurag@Gurome » Thu Feb 24, 2011 9:47 pm
5 machines - 3 jobs - 7 hours
5 machines - 1 job - 7/3 hours (as 5 machines will take less time to do 1 job as compared to 3 jobs, so we divide)
1 machine - 1 job - 7*5/3 hours (as 1 machine will take more time to complete 1 job as compared to 5 machines, so we multiply)

Now, 2 machines - 1 job - (7*5)/(3 * 2) hours
So, 2 machines - 5 jobs - (7*5*5)/(3 * 2) hours = 175/6 hours = 29 1/6 hours or 29 hours 10 minutes

The correct answer is E.
Last edited by Anurag@Gurome on Thu Feb 24, 2011 10:07 pm, edited 1 time in total.
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by manpsingh87 » Thu Feb 24, 2011 9:47 pm
sal_xcool wrote:If 5 machines can do 3 jobs in 7 hours, how long will it take 2 machines to do 5 jobs? Assume all jobs and
machines are equal.

A. 5 hours, 10 minutes
B. 11 hours, 40 minutes
C. 12 hours, 30 minutes
D. 18 hours, 40 minutes
E. 29 hours, 10 minutes

OA E

I always have problem with work problems.
I don't know what the best strategy is to tackle these problems. Using the work formula or logic.
When I look at this question, I have no clue how to use the work formula.
Any suggestion would be greatly appreciated.
7x(5/2)x(5/3) = 29 hours,10 minutes option E
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by GMATGuruNY » Thu Feb 24, 2011 10:05 pm
sal_xcool wrote:If 5 machines can do 3 jobs in 7 hours, how long will it take 2 machines to do 5 jobs? Assume all jobs and
machines are equal.

A. 5 hours, 10 minutes
B. 11 hours, 40 minutes
C. 12 hours, 30 minutes
D. 18 hours, 40 minutes
E. 29 hours, 10 minutes

OA E

I always have problem with work problems.
I don't know what the best strategy is to tackle these problems. Using the work formula or logic.
When I look at this question, I have no clue how to use the work formula.
Any suggestion would be greatly appreciated.
Plug in that the rate for each machine = 3 units/hour. (3 is a good number because it will allow us to easily divide the total work completed into 3 equal jobs.)
Thus, 5 machines produce 5*3 = 15 units per hour.
Over 7 hours, 7*15 = 105 units are produced.
Thus, each of the 3 jobs = 105/3 = 35 units.
Units produced in 5 jobs = 5*35 = 175 units.
Rate for 2 machines = 2*3 = 6 units per hour.
Time for 2 machines to produce 175 units = w/r = 175/6 = 29 hours, 10 minutes.

The correct answer is E.
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by sal_xcool » Thu Feb 24, 2011 10:05 pm
Anurag@Gurome wrote:5 machines - 3 jobs - 7 hours
5 machines - 1 job - 7/3 hours (as 5 machines will take less time to do 1 job as compared to 3 jobs, so we divide)
1 machine - 1 job - 7*5/3 hours (as 1 machine will take more time to complete 1 job as compared to 5 machines, so we multiply)

Now, 2 machines - 1 job - (7*5)/(3 * 2) hours
So, 2 machines - 5 jobs - (7*5*5)/(3 * 2) hours = 175/6 hours = 29 1/6 hours or 29 hours 10 minutes

The correct answer is C.

Thank you for your quick and awesome explanation.

I think you meant the correct answer is E not C.
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by Anurag@Gurome » Thu Feb 24, 2011 10:08 pm
sal_xcool wrote:
Anurag@Gurome wrote:5 machines - 3 jobs - 7 hours
5 machines - 1 job - 7/3 hours (as 5 machines will take less time to do 1 job as compared to 3 jobs, so we divide)
1 machine - 1 job - 7*5/3 hours (as 1 machine will take more time to complete 1 job as compared to 5 machines, so we multiply)

Now, 2 machines - 1 job - (7*5)/(3 * 2) hours
So, 2 machines - 5 jobs - (7*5*5)/(3 * 2) hours = 175/6 hours = 29 1/6 hours or 29 hours 10 minutes

The correct answer is C.

Thank you for your quick and awesome explanation.

I think you meant the correct answer is E not C.
Yes, you are right, I meant E, have edited the earlier post. Thanks for informing about the typo.
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