The Diaz family and the Nguyen family each used their sprinklers last summer. The water output rate for the Diaz family's sprinkler was 30L per hour. The water output rate for the Nguyen family's sprinkler was 25L per hour. The families used their sprinklers for a combined total of 45 hours, resulting in a total water output of 1225L. How long was each sprinkler used?
(D * 30) + (N * 25) = 1225
D + N = 45
To determine how long each sprinkler was used, we can set up a system of equations.
Let's assume that the Diaz family used their sprinkler for 'x' hours, and the Nguyen family used their sprinkler for 'y' hours.
According to the problem, the water output rate for the Diaz family's sprinkler is 30L per hour. So, the Diaz family's total water output would be 30x liters.
Similarly, the water output rate for the Nguyen family's sprinkler is 25L per hour. So, the Nguyen family's total water output would be 25y liters.
We know that the combined total water output of the two families is 1225L, so we can write the equation:
30x + 25y = 1225 ---(Equation 1)
We also know that the total time the families used their sprinklers is 45 hours, so we can write another equation:
x + y = 45 ---(Equation 2)
Now, we need to solve this system of equations simultaneously to find the values of 'x' and 'y'.
Let's rearrange Equation 2 to express one variable in terms of the other. We can subtract 'y' from both sides:
x = 45 - y
Now, substitute this value of 'x' in Equation 1:
30(45 - y) + 25y = 1225
Simplify the equation:
1350 - 30y + 25y = 1225
Combine like terms:
-5y = 1225 - 1350
-5y = -125
Divide both sides by -5:
y = -125 / -5
y = 25
Now, substitute this value of 'y' back into Equation 2 to find 'x':
x + 25 = 45
Subtract 25 from both sides:
x = 45 - 25
x = 20
Therefore, the Diaz family used their sprinkler for 20 hours, and the Nguyen family used their sprinkler for 25 hours.