Question

A tank has two inlet pipes and one outlet pipe. The inlet pipes can fill the tank in 4 hoursand 10 hours. The outlet pipe can drain the tank in 2 hours. One day the outlet pipe was leftopen as the empty tank was being filled. Will the tank ever be full? If so, how long will ittake to fill the tank? If not, explain why not.

Answer 1

The two inlet pipes can fill the tank in 4 hours and 10 hours.

The work done by the inlet pipes per hour is calculated to be:

`\Rightarrow(1)/(4)+(1)/(10)=(7)/(20)\text{ units per hour}`

The outlet pipe drains the tank in 2 hours. The work done will be:

`\Rightarrow(1)/(2)\text{ units per hour}`

Therefore, if both inlet pipes and the outlet pipes are opened at the same time, the work done by the pipes combined will be:

`\Rightarrow(7)/(20)-(1)/(2)=-(3)/(20)\text{ units per hour}`

Since the work done to fill the tank is negative, it means that the tank will never get full as it empties faster than it fills up.