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!

[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).

Cheers,
Brent

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.

GMAT assassins aren't born, they're made,
Rich