Question

The Faners family and the Edwards family each used their sprinklers last summer. The water output rate for the Edwards family's sprinkler was 40 L per hour. The water output rate for the Hayes family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 60 hours, resulting in a total water output of 2025 L. How long was each sprinkler used?

Answer 1

Edwards family: 35 hours

Hayes family: 25 hours

Explanation:

Given the two variables and two sets of data, you can set up a system of equations and substitution to solve for one variable first and then the other.

Based on the output rate for each sprinkler and the total water output:

40x + 25y = 2025, where 'x' is the number of hours of the Edwards sprinker and 'y' is the number of hours of the Hayes sprinkler

Based on the combined total of 60 hours

x + y = 60

Solving the second equation for 'x': x = 60-y

Substitute the expression '60 - y' in for 'x' in the first equation:

40(60 - y) + 25y = 2025

Distribute: 2400 - 40y + 25y = 2025

Combine like terms: -15y = -375

Divide and solve for 'y': y = 25

Solve for 'x': X = 60 - 25 = 35