Question

two pipes can fill a cistern separately in 24 and 40 minutes respectively and waste pipe can drain off 30 gallons per minute. if all the three pipes are open the cistern fills in one hour. what is capacity of the cistern?

Answer 1

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your answer in pic

Answer 2

Answer:

Capacity of the cistern is 600 gallons.

Step-by-step explanation:

The pipe A can fill in 24 minutes

Pipe A can fill tank in 1 minute = $\frac{1}{24}$

The pipe B can fill in 40 minutes

Pipe B can fill tank in 1 minute = $\frac{1}{40}$

Let pipe C can empty in x minutes.

Pipe C can empty tank in 1 minute = $\frac{1}{x}$

Together they can fill tank in 1 minute = $\frac{1}{24}+\frac{1}{40}-\frac{1}{x}$

We are given that  if all the three pipes are open the cistern fills in one hour.

So, Together they can fill tank in 1 minute = $\frac{1}{60}$

$\frac{1}{24}+\frac{1}{40}-\frac{1}{x}=\frac{1}{60}$

$\frac{1}{x}=\frac{1}{20}$

So, C can empty full tank in 20 minutes

In 1 minute C can drain off water = 30 gallons

So, In 20 minute C can drain off water = 30 * 20 = 600 gallons

Hence capacity of the cistern is 600 gallons.