Question

It takes 20 hours to fill the pool using the first hose. It takes 16 hours to fill the pool using the second hose. How long would it take if you used both?

Answer 1

8 and 8/9 hours

Explanation:

The rate of filling for the first hose is (1 pool/20 hrs)

The rate of filling for the second hose is (1 pool/16 hrs)

Let t= time to fill pool using both hoses

1/120 + 1/16 = 1/t

Multiply both sides by 320 t (which is 20*16)

300t/20 + 302t/16 = 320t/t

16t +20t = 320

36t = 320

t= 8.8888888 = 8 and 8/9

Answer 2

Answer: 8
`(8)/(9)` hours

Explanation:

Let x represent the time it takes if both are used.

The unit time it takes to fill the pool using the first house is 1/20 and also the unit time it takes to fill the pool using the second house is 1/16 , therefore:

1/16 + 1/20 = 1/x

`(4+5)/(20)` =
`(1)/(x)`

`(9)/(80)` =
`(1)/(x)`

Therefore

x =
`(80)/(9)`

Therefore, it takes 8
`(8)/(9)` hours using both houses