Question

The Gray family and the Thompson family each used their sprinklers last summer. The water output rate for the Gray family's sprinkler was 40 L per hour. The water output rate for the Thompson family's sprinkler was 20 L per hour. The families used their sprinklers for a combined total of 75 hours, resulting in a total water output of 2300 L . How long was each sprinkler used?

Answer 1

Gray family's sprinkler was used for 40 hours.

Thompson family's sprinkler was used for 35 hours.

Explanation:

The Gray family and the Thompson family each used their sprinklers last summer.

Let x= amount of time in hours that the Gray family's sprinkler was used.

Let y = amount of time in hours that the Thompson family's sprinkler was used.

The water output rate for the Gray family's sprinkler was 40 L per hour. The water output rate for the Thompson family's sprinkler was 20 L per hour. This means that the combined number of hours that both family's used their sprinklers is 40x + 20y

The families used their sprinklers for a combined total of 75 hours, resulting in a total water output of 2300 L .

This means

x + y = 75

40x + 20y = 2300 - - - - - - - -1

Substituting x = 75 -y into equation 1,

40 ( 75 - y ) + 20y = 2300

3000 - 40y + 20y = 2300

-40y + 20y = 2300 - 3000

-20y = -700

y = 700/20 = 35 hours

x = 75 - y

x = 75 -35 = 40 hours