Question

An inlet pipe on a swimming pool can be used to fill the pool in 30 hours. The drain pipe can be used to empty the pool in 48 hours. If the pool is 1/5 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?

Answer 1

Since both pipes are opened, you must find the net rate of inflow because some water is coming in at rate of 1/30 and some water is being drained at rate of 1/48.

Net rate = 1/30 - 1/48 = 8/240 - 5/240 = 3/240 = 1/80

This means the pool is adding water at a rate of 1/80 per hour.

To fill the pool you need 4/5 since it is starting 1/5 of the way full.
Rate*time = amount of water
1/80 * time = 4/5 pool
time = (4/5)/(1/80) = 80*(4/5) = 64

Final answer: It will take 64 hours to fill the pool.

Answer 2

The time taken to fill the swimming pool is 64 hours.

What is a word problem?

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Time taken to fill the swimming pool = 1/30 hours

Time taken to drain the swimming pool = 1/48 hours

The pool is 1/5 filled, then the remaining is 4/5.

The combined rate = $\frac{1}{30} -\frac{1}{48}$

⇒ $\frac{18}{(30)(48)}=\frac{1}{80}$

Let x be the time taken to fill the swimming pool.

The time taken to fill the swimming pool is

$(Rate)(time)=workdone$

⇒ $\frac{1}{80}x=\frac{4}{5}$

⇒ $x=\frac{(80)(4)}{5}$

⇒ $x=\frac{320}{5}$

⇒ $x=64$

Hence we can conclude that the time taken to fill the swimming pool is 64 hours.

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