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,
-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.