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

If B is the time the Barnes family used their sprinkler, and T the time the Trans family used theirs, the amount of water for the respective families are 35B and 40T.

B+T=60 total time, so B=60-T.

35B+40T=2300 total amount of water.

35(60-T)+40T=2300,

2100-35T+40T=2300,

5T=200, T=200/5=40 hours, so B=60-40=20 hours.

The Barnes family used their sprinkler for 20 hours and the Trans family for 40 hours.