Question

A water tank can be filled by an inlet pipe in 10 hours. It takes 2 times as long for the outlet pipe to empty the tank.How long will it take to fill the tank if both pipes are open?

Answer 1

it will take 20 hours to fill the tank if both pipes are open

Step-by-step explanation:

The time it takes to fill the tank = 10 hours

In 1 hour, it will take = 1/10 hours

The time it takes for the outlet to empty the tank = 2 times the time it takes to fill the tank

The time it takes for the outlet to empty the tank = 2 × 10 = 20 hours

In 1 hour, it will take = 1/20 hours

If both pipes are open, let the time it will take to fill the tank be t hours

In 1 hour = 1/t hours

The change in the amount in the tank is equal to the time it will take to fill the tank

1/10 - 1/20 = 1/t

`\begin{gathered} (1)/(10)-(1)/(20)=(1)/(t) \\ \frac{2(1)\text{ -1(1)}}{20}=(1)/(t) \\ (2-1)/(20)=(1)/(t) \\ \end{gathered}`
`\begin{gathered} (1)/(20)=(1)/(t) \\ \text{cross multiply:} \\ 1(t)\text{ = 1(20)} \\ t\text{ = 20} \end{gathered}`

Hence, it will take 20 hours to fill the tank if both pipes are open