Question

24. A tank can be filled by a pipe in 30 minutes and emptied by another pipe in 50 minutes. How many minutes will it take to fill the tank if both pipes are open?

Answer 1

Answer:

75 minutes

Step-by-step explanation:

The rate at which the tank is filled up, F, and emptied, E, are respectively:

$F=\frac{V}{30}*60 = 2V/hour\\E=\frac{V}{50}*60 = 1.2V/hour$

Since V is the full volume of the tank, the time required to fill the tank if both pipes are open is given by:

$F-E=2V/hour-1.2V/hour = 0.8V/hour\\t= \frac{1}{0.8}=1.25\ hours = 75\ minutes$

It will take 75 minutes to fill the tank if both pipes are open.