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 = 1275 ... equation 1

x + y = 45 ... equation 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