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?

Question

asked Aug 9, 2021 35.5k views

1 Answer

Matthew Ruddy · Answer 1 · 2021-08-12T18:35:43+0000

Answer:

75 minutes

Explanation:

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

$F=(V)/(30)*60 = 2V/hour\\E=(V)/(50)*60 = 1.2V/hour$

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

$F-E=2V/hour-1.2V/hour = 0.8V/hour\\t= (1)/(0.8)=1.25\ hours = 75\ minutes$

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