[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
Brent Hanneson - Creator of GMATPrepNow.com
