Question

The Henderson family and the Tran family each used their sprinklers last summer. The Henderson family's sprinkler was used for 15 hours. The Tran family's sprinkler was used for 40 hours. There was a combined total output of 1800L of water. What was the water output rate for each sprinkler if the sum of the two rates was 70L per hour?
Henderson family’s sprinkler: __ L per hour
Tran family’s sprinkler: __ L per hour

Answer 1

You have to create a system of equations in order to solve this, one based on total output and one based on output of each family's sprinkler.  The first equation is based on the total output according to how many hours each sprinkler ran.  Let's use H for the Henderson's and T for the Tran's. The equation for the total output is:
15H + 40T = 1800
That means that the Henderson's ran their sprinkler for 15 hours using H amount of water, and the Tran's ran their sprinkler for 40 hours using T amount of water, and that the total amount between the 2 families was 1800.
The next equation is based on each individual family's use of water per hour.
H + T = 70
That means that the Henderson's and the Trans together used 70 L per hour.
Solve the second equation for either variable (I picked H):
H = 70 - T
Now sub that value in for H in the second equation:
15(70 - T) + 40T = 1800
Now we will distribute the 15 into the parenthesis. The reason for that substitution is because we have 2 unknowns originally, an unknown H and an unknown T, and we can't solve an equation with 2 unknowns. The substitution gave us the equation in terms of T only.
1050 - 15T + 40T = 1800
1050 + 25T = 1800
25T = 750
T = 30
Now that we have a value for T, sub it in to the simple equation H + T = 70 to get H + 30 = 70, so H = 40