Answer:
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