Question

Direct variation?

Answer 1

see a solution process below;

Explanation:

From the question;

Let, `n = "no of water pumps"`

`t = "time"`

`3n -> 8hrs`

`4n -> xhrs`

Since they flow at same rate therefore, it takes a single pump;

`n = 8/3` pump per hour to fill a pool

For four pumps it would take;

`4n -> 8/3 xx 1/4`

`4n -> 32/12`

`4n -> 3hrs`

Hence it is an inverse variation, because the lesser more the pump, the lesser the time the pool gets filled up..

Hence we have;

`n prop 1/t`

`n =k/t`

Where, `k` is constant..

Initially we have;

`n = 3 and t = 8`

`n = k/t`

`3 = k/8`

`k = 3 xx 8`

`k = 24`

Hence we have;

`n = 24/t`

Making it, the less the `t` value becomes, the more the `n` value..

In other words, the less the time to fill a pool the more the number of pumps vice versa..

In summary

The quantity varies inversely. The constant variation is `24`. Four pumps need `3hrs` to fill a swimming pool..

Hope this helps!