The Patterson family and the bell family each used their sprinklers last summer. The wayer output rate for the patterson family's sprinkler was 25 L per hour. The water output rate for the bell family's speinkler was 15 L per hour. The familiez used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1225 L. How long was each sprinkler used?
time of Bell's sprinklers --- x hrs
time of Patterson's ------- 65-x hrs
solve for x:
15x + 25(65-x) = 1225
To determine how long each sprinkler was used, we can set up a system of equations.
Let's assume that the Patterson family used their sprinkler for x hours, and the Bell family used their sprinkler for y hours.
From the given information, we can set up the following equations:
1. The water output for the Patterson family: 25 L/hour * x hours = 25x L
2. The water output for the Bell family: 15 L/hour * y hours = 15y L
3. The total water output from both families: 25x L + 15y L = 1225 L
4. The total time both families used their sprinklers: x hours + y hours = 65 hours
We now have a system of equations:
25x + 15y = 1225 (Equation 1)
x + y = 65 (Equation 2)
We can solve this system of equations by either substitution or elimination method.
Let's solve it using the elimination method:
Multiply Equation 2 by 25 to make the coefficients of x the same:
25x + 25y = 1625 (Equation 3)
Now subtract Equation 1 from Equation 3 to eliminate x:
25x + 25y - 25x - 15y = 1625 - 1225
Simplifying:
10y = 400
Divide both sides by 10:
y = 40
Substitute the value of y into Equation 2:
x + 40 = 65
Subtract 40 from both sides:
x = 25
Therefore, the Patterson family used their sprinkler for 25 hours, and the Bell family used their sprinkler for 40 hours.