The Pool Problem

Quote:

Originally Posted by Caity

Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 1/2 hours. How quickly can all three fill the pool together? I know the answer is 15 minutes... again I need to find a way to explain it...

Hi Caity,

Ah...the good old work problem.

Jim can fill the pool in 30 minutes. So, he fills 1/30 of the pool in 1 minute.

Sue can fill the pool in 45 minutes. So, she fills 1/45 of the pool in 1 minute.

Tony can fill the pool in 90 minutes. So, he fills 1/90 of the pool in 1 minute.

$\frac{1}{30}+\frac{1}{45}+\frac{1}{90}=\frac{1}{t}$

Now, solve for t.

If you multiply everything by t, the equation will look this way:

$\frac{1}{30}t+\frac{1}{45}t+\frac{1}{90}t=1$

You can find similar "work" problems and a pretty good explanation here: "Work" Word Problems

Also, here is a related thread in this forum: http://www.mathhelpforum.com/math-he...ng-172924.html