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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?

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pedrocarratore

Answer:

75 minutes

Step-by-step explanation:

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

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

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

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

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

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