Question

An inlet pipe can fill a tank in 10 hours. An outlet pipe can drain that sametank in 30 hours. The inlet valve is opened, but the outlet valve is accidentallyleft open. How long will it take to fill the tank with both valves open?

Answer 1

It will take 15 hours to fill the tank with both valves open

Explanation:

Given,

The time taken by inlet pipe to fill the tank = 10 hours,

So, work done by inlet pipe in one hour =
`(1)/(10)`,

Also, the time taken by outlet pipe to drain = 30 hours,

So, work done by outlet pipe in one hour =
`-(1)/(30)`,

( Note : Negative sign shows the draining )

Thus,the total work done in one hour

`=(1)/(10)-(1)/(30)`

`=(3-1)/(30)`

`=(2)/(30)`

`=(1)/(15)`

Hence, the time taken to fill the tank =
`\frac{1}{\text{Total work done in one hour}}`

`=(1)/(1/15)`

= 15 hours