Question

One hose can fill a goldfish pond in 36 ​minutes, and two hoses can fill the same pond in 20 minutes. Find how long it takes the second hose alone to fill the pond.

Answer 1

The time taken by the second hose alone to fill the pond is 45 minutes.

Explanation:

One hose can fill a goldfish pond in 36 ​minutes.

Let second hose can fill the pond alone in x minutes.

The part of goldfish pond filled by one hose in 1 minute is
`(1)/(36)`.

The part of goldfish pond filled by second hose in 1 minute is
`(1)/(x)`.

Two hoses can fill the same pond in 20 minutes.

The part of goldfish pond filled by both hose in 1 minute is
`(1)/(20)`.

`(1)/(36)+(1)/(x)=(1)/(20)`

`(x+36)/(36x)=(1)/(20)`

`20(x+36)=36x`

`20x+720=36x`

`720=36x-20x`

`720=16x`

`(720)/(16)=x`

`45=x`

Therefore, the time taken by the second hose alone to fill the pond is 45 minutes.

Answer 2

45 minutes

Explanation:

It is given that one hose can fill a goldfish pond in 36 minute

So the the first hose can fill goldfish pond
`(1)/(36)` per minute

When both fill together then they fill in 20 minutes

So the the both hose can fill goldfish pond
`(1)/(20)` per minute

Let Goldfish pond filled by second hose
`(1)/(x)` per minute

so
`(1)/(36)+(1)/(x)=(1)/(20)`

`(1)/(x)=(1)/(20)-(1)/(36)`

x=45 minutes