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The Woody family and the carter family each used their water sprinklers last summer. The water output rate for the wood familys sprinkker was 40L per hour.

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
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2 Answers

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.
 
This word problem first needs to be turned into equations to help you solve.
 
First, let's labele what we know.
Each family used a certain amount of water, so lets call the total time water used by the Carter family C and the total time water was used by the Woody family W. Since the total number oh hours that water was used for both families is given in the problem, we can make one equation: C+W =50 hr.
Next, we know the rate that each family used water, so multiplying a rate by a time will give us an amount of water usage in liters for each family. Since the Carters used 35 L per hour and the Woodys use 40 L per hour and total usage is 1900 L, our equation for total water usage is 35 L/hour *C + 40 L/ hour * W =1900 L.
 
Now that we have two equations and two unknowns, we can solve. The first equation becomes C= 50 hr.-W or W=50 hr.-C, we can use either variation of the equation to substitute into the second equation.
 
For this example, I will use the form W=50 hr.-C. Plugging this into the second original equation, we get:
(35 L/hr)*(C) + (40 L/hr)(50 hr. -C)= 1900 L
This becomes:
(35 L/hr)*(C) + (2000 L - 40L/ hr. *C)= 1900 L
Grouping like terms, we get:
 
2000 L+ (35 -40) L/hr *C = 1900 L
 
Solving for C,
 
5L/hr * C = 100 L
 
C= 20 Hours
 
Plugging this into C + W=50 hours, we can solve for the amount of water used by the Woody family.
 
20+W= 50 hours
W=30 Hours.