Question

The Carter family and the Tran family each used their sprinklers last summer. The water output rate for the Carter family's sprinkler was 35 L per hour. The

water output rate for the Tran family's sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 40 hours, resulting in a total water
output of 1100 L. How long was each sprinkler used?

Answer 1

Carter family - 25 hours

Tran family - 15 hours

Explanation:

We are going to be using variable C and T to represent the amount of hours each family used in total:

Because we know "The families used their sprinklers for a combined total of 40 hours", write the following equation:

`C+T=40` - Equation (1)

We also know the following equation:

`35C+15T=1100` - Equation (2)

Solve for T in equation (1):

`T=40-C`

Substitute this into equation (2)

`35C+15(40-C)=1100`

Distribute:

`35C+600-15C=1100`

Subtract 600 from both sides and simplify:

`20C=500`

Divide both sides by 20:

`C=25`

Substitute this back into equation (1):

`25+T=40`

Subtract 25 from both sides:

`T=15`

Therefore we know:

`C=25`

`T=15`