Answer:
Gray family's sprinkler was used for 40 hours.
Thompson family's sprinkler was used for 35 hours.
Step-by-step 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
