Please help me!!!!
The Cooper family and the Anderson family each used their sprinklers last summer. The water output rate for the Cooper family's sprinkler was
20L
per hour. The water output rate for the Anderson family's sprinkler was
25L
per hour. The families used their sprinklers for a combined total of
55
hours, resulting in a total water output of
1300L
. How long was each sprinkler used.
To solve this problem, we can use a system of equations.
Let's assume the Cooper family used their sprinkler for x hours and the Anderson family used their sprinkler for y hours.
The water output for the Cooper family's sprinkler is 20L per hour, so the total water output for the Cooper family is 20x liters.
Similarly, the water output for the Anderson family's sprinkler is 25L per hour, so the total water output for the Anderson family is 25y liters.
According to the problem, the combined total water output is 1300L, so we can write the equation:
20x + 25y = 1300 ----(1)
We also know that the total hours used is 55, so we can write another equation:
x + y = 55 ----(2)
Now we have a system of equations consisting of equations (1) and (2).
To solve this system, we can use the substitution method or elimination method.
Let's solve it using the substitution method:
From equation (2), we have x + y = 55 which implies x = 55 - y.
Now substitute x = 55 - y in equation (1):
20(55 - y) + 25y = 1300
1100 - 20y + 25y = 1300
5y = 1300 - 1100
5y = 200
y = 200/5
y = 40
Now, substitute the value of y back into equation (2):
x + 40 = 55
x = 55 - 40
x = 15
Therefore, the Cooper family used their sprinkler for 15 hours, and the Anderson family used their sprinkler for 40 hours.
a+c = 55
25a+20c = 1300
Now just solve for a and c.