Question

The Doe family is ready to fill their new swimming pool. It can be filled in 12 hours if they use their own water hose, and in 30 hours if they use Mr. Jones', their neighbor's water hose. How long will the Doe's take to fill their pool if the neighbor's hose is used along with their own?

Answer 1

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Answer 2

Ah, rate problems. I like rate problems :-)

The easiest way to tackle these is usually to find the rate of each hose, pump, widget, worker, etc.

The Doe family's hose will fill the pool in 12 hours, so the rate is 1 pool/12 hours.

The Jones family hose will fill the pool in 30 hours, so that rate is 1 pool/30 hours.

If you use both hoses together, the combined rate is 1/12 + 1/30

The total time to fill the pool with both hoses will be

\[\large\frac{1\text{ pool}}{\frac{1\text{ pool}}{12\text{ hours}} + \frac{1\text{ pool}}{30\text{ hours}}} = \text{___________ hours}\]