SOLUTION: The Peterson family and the Gonzales family each used their sprinklers last summer. The Peterson family's sprinkler was used for 20 hours. The Gonzales family's sprinkler was used

Question 875057: The Peterson family and the Gonzales family each used their sprinklers last summer. The Peterson family's sprinkler was used for 20 hours. The Gonzales family's sprinkler was used for 40 hours. There was a combined total output of 1800L of water. What was the water output rate for each sprinkler if the sum of the two rates was 55L per hour?
Peterson's family's sprinkler: L per hour
Gonzales family's sprinkler: L per hour
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Uniform rates situation, , R is a constant for each agent; v is volume in liters and t is time in hours. The rule for this uniform rates idea is equivalently .

Petersons: Let P = sprinkler rate.
Volume was P*20 liters.

Gonzalezes: Let G = sprinkler rate.
Volume was G*40 liters.

Combined volumes: liters.

Also given was that the combined rate for the two families' sprinklers was 55 liters per hour. This means, .

This feels like an unrealistic thing, because the two different sprinklers probably did not sprinkle simultaneously - even so, we have two equations and two unknown variables, P and G. Simplify the combined volume equation to , and we have the system:
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P+2G=90
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P+G=55
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Solve that system for P and G any way you want. Elimination would be a good way to start. G=35 and so P=20, liters per hour.
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