Question

The Gonzales family and the brown family each used their sprinklers last summer. The water output rate for the Gonzales family sprinkler was 35 L per hour. The water output rate for the brown family's sprinkler was 30 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1750 L. How long was each sprinkler used?

Answer 1

The Gonzales family used the water sprinkler for 20 hours

The Brown family used the water sprinkler for 35 hours

Explanation:

Let represent

Number of hours that the Gonzales family used the water sprinkler = x

Number of hours that the Brown family used the water sprinkler = y

The families used their sprinklers for a combined total of 55 hours

Hence,

x + y = 55 ...... Equation 1

x = 55 - y

The water output rate for the Gonzales family sprinkler was 35 L per hour.

35L × x = 35x

The water output rate for the brown family's sprinkler was 30 L per hour.

30L × y = 30y

The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1750 L.

Hence, we have:

35x + 30y = 1750..... Equation 2

Substitute x = 55 - y in Equation 2

35(55 - y) + 30y = 1750

1925 - 35y + 30y = 1750

Collect like terms

1925 - 1750 = 35y - 30y

175 = 5y

y = 175/5

y = 35 hours

Since:

x = 55 - y

x = 55 - 35

x = 20 hours

Since Number of hours that the Gonzales family used the water sprinkler = x,

The Gonzales family used the water sprinkler for 20 hours

Since number of hours that the Brown family used the water sprinkler = y,

Hence, the Brown family used the water sprinkler for 35 hours