Question

My old nemesis... Any brave word-problem slayers know how to tackle this nightmare for me?

Working together, two pumps can drain a certain pool in 4 hours. If it takes the older pump 9 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?

Answer 1

7.2 hours.

Answer 2

Do you mind briefly explaining your logic?

Answer 3

I do not mind at all!

Answer 4

Gee thanks!

Answer 5

This is a work problem. If the pumps do the job together in 4 hours, the ratio of hours to work is 1/4, meaning they can get 1/4 of the whole job done in one hour. If the old pump takes 9 hours to do the job alone, it can get 1/9 done in 1 hour. We need to find out how long it takes the new pump to do the job alone, so we will call that x.

Answer 6

\[\frac{ 1 }{ 9 }+\frac{ 1 }{ x }=\frac{ 1 }{ 4 }\]

Answer 7

to solve for x, you need to rid yourself of those pesky fractions, so we will multiply all the terms by the LCM of 36x. We then have this:

Answer 8

4x + 36 = 9x

Answer 9

Oh, thank you! I had set up that equation but subtracted 1/9 from 1/4 instead of doing the LCM.

Answer 10

And got a funky answer..

Answer 11

Can you see then how to solve for x?

Answer 12

funky isn't good! ; )

Answer 13

You are awesome on turning on light bulbs for people! Thank you for taking the time to enlighten me. Now I have actually learned something!

Answer 14

lol

Answer 15

Wow! Thank you so much for that!

Answer 16

lol on the funky...

Answer 17

Thanks for slaying my problem IMStuck :D

Answer 18

You bet!

Answer 19

lol again! Call me "The Slayer"...

Answer 20

You can probably tell I like English way over math :/ But yes, its true. This math problem has been killed :D