Question

The escobar family and the johnson family each used their sprinklers last month. The water output rate for the Escobar family's sprinkler was 30 gallons per hour. The water output rate for the Johnson family's sprinkler was 50 gallons per hour. The families used their sprinklers for a combined total of 32 hours, resulting in a total water output of 1320 gallons. How many hours was each family's sprinkler used?

Answer 1

The Escobar family's sprinkler was was used for 14 hours and the Johnson's for 18 hours.

Explanation:

I am going to solve this question by a system of equations.

We have that:

x is the number of hours that the Escobar's sprinkler was used.

y is the number of hours that the Johnsons' sprinkler was used.

The families used their sprinklers for a combined total of 32 hours

This means that
`x + y = 32`

Total water output of 1320 gallons.

Escobar 30 gallons a hour, Johnson 50. So

`30x + 50y = 1320`

From the first equation

`x = 32 - y`

`30x + 50y = 1320`

`30(32 - y) + 50y = 1320`

`960 - 30y + 50y = 1320`

`20y = 360`

`y = 18`

`x = 32 - y = 32 - 18 = 14`

The Escobar family's sprinkler was was used for 14 hours and the Johnson's for 18 hours.