Question

The Lewis family and the Rodriguez family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was 20L per hour. The water output rate for the Rodriguez family's sprinkler was 25L per hour. The families used their sprinklers for a combined total of 65hours, resulting in a total water output of 1425L How long was each sprinkler used?

Answer 1

This requires a system of equations, one to relate the number of hours each sprinkler was used in each family, and then one to relate the Liters of water put out by each family's sprinkler. The first equation, relating the number of hours requires us to add the hours that the Lewis family used their sprinkler to the number of hours the Rodriguez family used their sprinkler, both of which are unknown. So here's the first equation:
L + R = 65
That means that the use of the Lewis sprinkler plus the use of the Rodriguez sprinkler equals 65 hours.

Answer 2

We are told that the Lewis sprinkler put out 20 liters per hour and that the Rodriguez sprinkler put out 25 liters per hour to equal a total of 1425 liters. So the second equation is this:
20L + 25R = 1425
That means that the 20 liters that the Lewis family uses, added to the 25 liters that the Rodriguez family uses comes out to a total of 1425 liters.

Answer 3

Now we have our 2 equations:
L + R = 65
20L+25R=1425

Answer 4

Now we can solve the first equation for either the L or the R. Let's solve it for L.
L + R = 65 ---> L = 65 - R

Answer 5

Now we can put that L value into the second equation wherever we see an L and have that second equation in terms of R only. Like this: