He Scott family and the Cox family each used their sprinklers last summer. The water output rate for the Scott family's sprinkler was
35L
per hour. The water output rate for the Cox family's sprinkler was
25L
per hour. The families used their sprinklers for a combined total of
45
hours, resulting in a total water output of
1275L
. How long was each sprinkler used?

Scott's family sprinkler time = 15 hours

Cox's family sprinkler time = 30 hours

To check: 35x + 25y = 1275 = 35 (15) + 25 (30) = 1275

Explanation:

The Scott family and the Cox family each used their sprinklers last summer.

The water output rate for the Scott family's sprinkler was  35L  per hour.

The water output rate for the Cox family's sprinkler was  25L  per hour.

The families used their sprinklers for a combined total of  45  hours, resulting in a total water output of  1275L . How long was each sprinkler used

Let x represents Scott's family time

Let y represents Cox's family time

35x + 25y = 1275equation 1

x + y = 45equation 2

If x + y = 45, therefore x = 45 - y

substituting 45-y for x in equation 1

35(45-y) + 25y = 1275

1575 - 35y +25y = 1275

- 35y + 25y = 1275 - 1575

- 10y = - 300

y  = 30 hours

Substituting 30 for y in equation 2

x + 30 = 45

x = 15 hours

To check: 35x + 25y = 1275 = 35 (15) + 25 (30) = 1275

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