how long was each sprinkler used?

Question

The Bennett family and the Hill family each used their sprinklers last summer. The water output rate for the Bennett family's sprinkler was 25L per hour. The water output rate for the Hill family's sprinkler was 15L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1075L. How long was each sprinkler used?

Answer 1

Hi Tamara!

We will need to model the scenario with 2 separate equations because we need to solve for two unknowns. Let's say that the Bennett family uses their sprinkler for B hours and the Hill family uses theirs for H hours.

Equation #1

1. The problem tells us that the Bennett's sprinkler uses water at a rate of 25L per hour; so we can say that in B hours, the Bennet family uses 25B liters of water.
2. We're told that the Hill family's sprinkler uses 15L of water per hour; so we can say that in H hours, the Hill family uses 15H liters of water.
3. The problem states that, in total, the two families use a combined total of 1075L
4. Putting this all together, we can say 25B + 15H = 1075 (equation #1)

Equation #2

1. Since we're told that the two families use the sprinklers for a combined total of 55 hours, we can say that B+H=55

Solving:

We can solve by substitution or elimination. I'll use substitution by solving equation #1 for H, and then subbing that result into equation #2.

1. Solve equation #2 for H: B+H=55 -> H=55-B
2. Plug H=55-B into equation #1: 25B+15H=1075 -> 25B+15(55-B)=1075 -> 25B+825-15B=1075 -> 10B=250 -> B=25 hours
3. Use B=25, to solve for H in either equation: B+H=55 -> 25+H=55 -> H=30 hours

And you're done!