Solving a value mixture problem using a system of linear

Question

The Collins family and the Hughes family each used their sprinklers last summer. The Collins’s family’s sprinkler was used for 25 hours. The Hughes family’s sprinkler was used for 20 hours. There was a combined total output of 1500 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 65 L per hour?

Answer 1

Let c = Collins' rate and h = Hughes' rate.

25c + 20h = 1500

c + h = 65

Multiply the second equation by 20 and subtract it from the first equation

25c + 20h = 1500

20c + 20h = 1300

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5c + 0 = 200

c= 200/5

c = 40 L/hr

h = 25 L/hr