Acold water pipe can fill a swimming pool in 4 hours, and a hot water pipe in 6 hours. if cold water pipe is turned on and hot water pipe is turned on 3 hours later then how long will it take them to fill the pool together?

If cold water pipe is turned on and hot water pipe is turned on 3 hours later then it will take 36 minutes (or 0.6 hr) to them to fill the pool together.

Step-by-step explanation:

Given :

Cold water pipe can fill a swimming pool in 4 hours, and a hot water pipe in 6 hours.

Solution :

Let's say the swimming pool is x gallons.

The flow rate of the cold water pipe is,

The flow rate of the hot water pipe is,

If the cold water pipe is turned on for three hours, the volume of water is:

The time to fill the rest of the pool with both the cold and hot water pipes is,

= 0.6 hr

If cold water pipe is turned on and hot water pipe is turned on 3 hours later then it will take 36 minutes (or 0.6 hr) to them to fill the pool together.

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0.6 hours

Step-by-step explanation:

Let's say the swimming pool is 12,000 gallons.

The flow rate of the cold water pipe is:

12000 gal / 4 hr = 3000 gal/hr

The flow rate of the hot water pipe is:

12000 gal / 6 hr = 2000 gal/hr

If the cold water pipe is turned on for three hours, the volume of water is:

3000 gal/hr × 3 hr = 9000 gal

That leaves 3000 gallons.  The time to fill the rest of the pool with both the cold and hot water pipes is:

3000 gal / (3000 gal/hr + 2000 gal/hr) = 0.6 hr

It takes 0.6 hours (36 minutes).

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