Question

It takes a smaller hose 3 times as long to fill a small swimming pool as it does a larger hose. It takes both hoses working together 15 minutes to fill the swimming pool. How long will it take the smaller hose to fill the pool by itself?

Answer 1

60 minutes

Explanation:

Let the Larger hose take time to fill the swimming pool= x minutes

Than, time taken by smaller tank to fill the same swimming full tank= 3 x minutes

If both hoses work together time taken by both of them= 15 minutes

A.T.Q

`(1)/(x)` +
`(1)/(3x)` =
`(1)/(15)`

`(3+1)/(3x)` =
`(1)/(15)`

`(4)/(3x)`=
`(1)/(15)`

x=
`(15)/(3)`× 4

x= 20 minutes

Larger hose take time to fill the swimming pool= 20 minutes

Than, time taken by smaller tank to fill the same swimming full tank= 3 x = =3× 20= 60 minutes

Hence. the correct answer is 60 minutes

Answer 2

60 minutes.

Explanation:

Let t represent time taken by larger hose in minutes to fill the pool.

Part of pool filled by larger hose in one minute would be
`(1)/(t)`.

We have been given that it takes a smaller hose 3 times as long to fill a small swimming pool as it does a larger hose, so smaller hose will take
`3t` minutes to fill the pool.

Part of pool filled by smaller hose in one minute would be
`(1)/(3t)`.

We are also told that it takes both hoses working together 15 minutes to fill the swimming pool, so part of pool filled by both hoses in one minute would be
`(1)/(15)`.

`(1)/(t)+(1)/(3t)=(1)/(15)`

`(1)/(t)\cdot 15t+(1)/(3t)\cdot 15t=(1)/(15)\cdot 15t`

`15+5=t`

`t=20`

So it will take 20 minutes for the larger hose to fill the pool alone.

Since smaller hose takes 3 times as long to fill a pool, so 3 times 20 would be 60.

Therefore, it will take 60 minutes for the smaller hose to fill the pool alone.