the water output rate for the Carter family sprinkleeer was 35L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 19ooL. How long was each sprinkler used? For the family and the Carter family in hours

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.