The Jenkins family and the Alexander family each used their sprinklers last summer. The water output rate for the Jenkins
family's sprinkler was 25 L per hour. The water output rate for the Alexander family's sprinkler was 40 L per hour. The
families used their sprinklers for a combined total of 45 hours, resulting in a total water output of 1425 L. How long was
each sprinkler used?

To solve this problem we need to set up two equations. We know the rates of each sprinkler's output and how much total water was output. We know how many hours the sprinklers were on. We are looking for how long each sprinkler was used.

We can make a represent hours because we know the rate of sprinkler's output is per hour.

25a+40b=1425

a+b=45

Now to solve this system of equations we need to isolate a variable on one equation to plug into the other.

a+b=45

a=45-b

Now we can plug this in for a in the other equation.

25a+40b=1425

25(45-b)+40b=1425

Distribute 25 into the parenthesis.

1125-25b+40b=1425

1125+15b=1425

15b=300

b=20

Now we know that the Alexander family used their sprinklers for 20 hours. We can plug this back into the other equation to find b.

a+b=45

a+20=45

a=25

The Jenkins used the sprinklers for 25 hours, and the Alexanders used them for 20 hours.