It’s a hot summer day. Darius is babysitting and has promised his sweet little sister that he will fill her wading pool. He plans to soak his feet in the water as he sips a cool soda and watch little sister as she plays in the water. Sounds great, right? All he needs to do is get the pool filled. Unfortunately, little sister is impatient and starting to whine. Darius has a hose ready in the backyard to fill the pool, but he decides he will also drag the hose from the front-yard, so the two hoses can work together to fill the pool faster. Nobody wants their darling little sister to be unhappy!

Darius knows from experience that if he only uses one hose at a time, the front-yard hose takes 10 minutes longer to the fill the pool than the back-yard hose. With the two hoses working together, the pool is filled in 12 minutes. Once Darius is comfortable with his toes dangling in the water, he starts to wonder how long it would have taken to fill the pool if he had only used one of the hoses.

Darius thinks, “Hmmm. Usually when I think about how long it takes to do something I have to think about the rate it is going.”

1. What is the combined rate of the two hoses in filling the pool? What are the units of the rate?

2. What is the rate of the back-yard hose when it is working alone? What are the units of the rate?

Take the time to fill with two hoses, double that to get the time for two hoses with equal rates. 24 minutes. But one takes 10 minutes more, so split that. 24 + 5 is 29 minutes. 10 less is 19 minutes. Or try 27 and 17.

If you assume a typical kiddie pool 4 ft diameter and 1 ft deep, not quite full, that would hold around 84 gallons.

84÷12 = 7 gallons per minute.

84÷ 17 = about 4.9 gpm

84 ÷ 27= 3.1 gpm

So 16 and 6 might be possible times to try for realistic rates.

I realize this is not a complete answer, but it might help.