Question

The Murphy family and the Edwards family each used their sprinklers last summer. The water output rate for the Murphy family's sprinkler was 20L per hour. The water output rate for the Edwards family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 2000L . How long was each sprinkler used?

Answer 1

Time used total: 50 hours.W+C = 50 (1) Total water used is 1900 L.Woody family used: 40W; Carter family used 35C.Equation showing how much water both families used:40W + 35 C =1900. (2) We have a system with two equations and two variables. We can use substitution method to solve the system. From equation (1) we express W:W=50 - C. (1a) We substitute the variable in equation (2):40(50 - C) +35C =1900. We open the parenthesis2000 -40C +35C =1900, We combine like terms2000 -5C =1900, We subtract 2000 from both sides of the equation-5C = 1900 - 2000, We simplify-5C = -100, We divide by -5C = 20. We substitute the values of C in the equation (1a) and find the value of W:W = 50 - C,W = 50 -20 =30. The Woody family used water for 30 hours and the Carter family used water for 20 hours.We check our work to be sure we did not make any mistakes:Total water used: 40 x 30 + 35 x 20 = 1200 + 700 = 1900 L.