Question

The Hayes family and the Rodrigues family use their sprinklers last summer. The water output rate for the Hayes family sprinkler was 15 L per hour. The water Output rate for the Rodriguez family speakers is 30 L per hour.Families used their sprinklers for a combined total of 75 hour result in a total water of output of 1725 L how long was a sprinkler used?

Answer 1

• Hayes family: 35 hours
• Rodrigues family: 40 hours

Explanation:

Let x and y represent the usage hours by the Hayes and Rodrigues families, respectively. The problem statement gives us relations that can be used to write equations for volume of use and for total hours.

15x +30y = 1725 . . . . . total liters of use

x + y = 75 . . . . . . . . . total hours of use

The second equation lets us write an expression for y:

y = 75 -x

This can be substituted into the first equation to give ...

15x +30(75 -x) = 1725

-15x + 2250 = 1725 . . . . . . simplify

-15x = -525 . . . . . . . . . . . subtract 2250

x = 35 . . . . . . . . . . . . . . divide by -15

y = 75 -35 = 40

The Hayes family used their sprinklers for 35 hours; the Rodrigues family used theirs for 40 hours.