Question

The Moore family and the Bell family each used their sprinklers last summer. The water output rate for the Moore family's sprinkler was 15L per hour. The water output rate for the Bell family's sprinkler was 30L per hour. The families used their sprinklers for a combined total of 75 hours, resulting in a total water output of 1725L. How long was each sprinkler used?

Answer 1

Answer: the Moore family used their sprinkler for 35 hours.

the Bell family used their sprinkler for 40 hours.

Step-by-step explanation:

Let m represent the number of hours for which the Moore family used their sprinkler.

Let b represent the number of hours for which the Bell family used their sprinkler.

The families used their sprinklers for a combined total of 75 hours. It means that

m + b = 75

The water output rate for the Moore family's sprinkler was 15L per hour. The water output rate for the Bell family's sprinkler was 30L per hour. The total water output for both families was 1725L. It means that

15m + 30b = 1725- - - - - - - - - - --1

Substituting m = 75 - b into equation 1, it becomes.

15(75 - b) + 30b = 1725

1125 - 15b + 30b = 1725

- 15b + 30b = 1725 - 1125

15b = 600

b = 600/15

b = 40

m = 75 - b = 75 - 40

m = 35