Can you explain this algebra problem to me?

Question

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?

answer: 15 minutes

I don't understand how to work these types of problems. If you could explain it to me I'd be very happy :)

Answer 1

This type of problem comes up all the time and you have to remember how they're done. You set up this equation where x represents the time:

x/30 + x/45 + x/90 = 1

Clear fractions by multiplying everything by 90

3x + 2x + x = 90
6x = 90

so x = 15 minutes

Answer 2

If Jim could fill 1 pool in 30 minutes, it stands to reason he could fill 1/30 of the pool in 1 minute, as he'd be filling 30/30 of the pool (the entire pool) in the full 30 minutes. Similar logic would have Sue filling 1/45 of the pool in 1 minute and Tony filling 1/90 of the pool in 1 minute.

So working in concert, the three of them could fill

1/30 + 1/45 + 1/90
= 3/90 + 2/90 + 1/90
= 6/90
= 1/15 in one minute

Using the original logic and going backwards, they could then fill the entire pool in 15 minutes.