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Rate problem

by [email protected] » Fri Jul 04, 2014 8:03 am
Working together, 7 identical pumps can empty a pool in 6 hours. How many hours will it take 4 pumps to empty the same pool?

I was trying to solve this question the following way pls tell me whts wrong:

7 pumps do it in 6 hrs therefore 1 pump will do it in 6/7 hrs and 4 pumps can do it in (6/7)*4hrs
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by GMATinsight » Fri Jul 04, 2014 8:14 am
Working together, 7 identical pumps can empty a pool in 6 hours. How many hours will it take 4 pumps to empty the same pool?
Hi Shibsriz,

The mistake is "Number of Pumps" required and "Time taken by them to empty the tank" are Inversely Proportional which you are taking as directly proportional.

Inversely proportional means that Decrease in Number of Pumps by some factor will require Increase in the number of Hours by same factor

Therefore,
If 7 identical pumps can empty a pool in 6 hours
then 1 Pump can empty a pool in 6x7 = 42 hours

Therefore 4 Pump can empty a pool in 6x7/4 = 42/4 = 10.5 hours
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by [email protected] » Fri Jul 04, 2014 8:23 am
yep thanks silly mistake!
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by ceilidh.erickson » Fri Jul 04, 2014 9:25 am
Before solving any word problem, it's a good idea to do a "gut-check" first - ask yourself what sort of answer would be logical. Whenever you're looking at a rate problem, fewer workers will need more time to complete the task. So 4 pumps should always take longer than 7 pumps. If you got an answer that was less than 6 hrs, that was your clue that your setup was wrong!
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by Brent@GMATPrepNow » Fri Jul 04, 2014 10:00 am
[email protected] wrote:Working together, 7 identical pumps can empty a pool in 6 hours. How many hours will it take 4 pumps to empty the same pool?
For work questions, there are two useful rules:

Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.

Let's use these rules to solve the question. . . .

7 identical pumps can empty a pool in 6 hours.
By Rule #1, we know that IN 1 HOUR, 7 pumps can empty 1/6 of the pool.
From this, we can conclude that IN 1 HOUR, 1 pump can empty 1/42 of the pool.

How many hours will it take 4 pumps to empty the same pool?
If 1 pump can empty 1/42 of the pool IN 1 HOUR, then 4 pumps can empty 4/42 of the pool IN 1 HOUR.
By Rule #2, we can conclude that 4 pumps will empty the ENTIRE pool in 42/4 hours ( = 10.5 hours).

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by [email protected] » Fri Jul 04, 2014 1:52 pm
Hi shibsriz,

These types of rate questions can be solved in a variety of ways (as evidenced by the various responses to your question). Here's another way of dealing with this question....

Since we have 7 machines working for 6 days, there are 7x6 = 42 machine-days of work required to complete the job.

Those 42 machine-days of work can be spread over any number of machines (and by extension, over any number of days).

1 machine would need 42 days to complete the job
2 machines would need 21 days to complete the job
3 machines would need 14 days to complete the job
Etc.

In that same way, to get the job done in....
1 day would require 42 machines
2 days would require 21 machines
3 days would require 14 machines
Etc.

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