Solving a value mixture problem using a system of linear equations

Question

The Barnes family and the Tran family each used their sprinklers last summer. The water output rate for the Barnes family's sprinkler was 35L per hour. The water output rate for the Tran family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 60 hours, resulting in a total water output of 2300L. How long was each sprinkler used?

Answer 1

x+y = 60

35x + 40y = 2300

35x + 40(60-x) = 2300

35x + 2400 - 40x = 2300

-5x = -100

x = 20

then y = 40