Question

The Garcia family and the Johnson family each used their sprinklers last summer. The Garcia family's sprinkler was used for 20 hours. The Johnson family's sprinkler was used for 25 hours. There was a combined total output of 1175 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 55 L per hour?

Answer 1

W is the time Woody family used sprinkler.

C is the time Carter family used sprinkler.

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 parenthesis

2000 -40C +35C =1900,

We combine like terms

2000 -5C =1900,

We subtract 2000 from both sides of the equation

-5C = 1900 - 2000,

We simplify

-5C = -100,

We divide by -5

C = 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.