Question

The Wong family and the Nguyen family each used their sprinklers last summer. The water output rate for the Wong familys sprinkler was 35 L per hour. The water output for the Nguyen familys sprinkler was 20 L per hour. The families used their spirit for a combined total of 75 hours, resulting in a total water output of 2100 L. How long was each sprinkler used?

Answer 1

Let W be the time of the wong family and N the time of the Nguyen family. We are told that the output rate of the Wong family is 35 L/h and the output for the Nguyen family is 20 L/h, if the total water output is 2100 L, then we can write this mathematically as:

`35W+20N=2100,(1)`

Where "35W" is the total water output of the wong family and "20N" is the total water output of the Nguyen family. The two outputs combined must be 2100. We are also told that the total time is 75 hours, therefore we have:

`W+N=75,(2)`

We get a system of two equations and two variables. We can solve for "W" in equation (2), by subtracting "N" from both sides:

`W=75-N`

Now we can replace this value in equation (1):

`35(75-N)+20N=2100`

Now we apply the distributive property:

`2625-35N+20N=2100`

Now we add like terms;

`2625-15N=2100`

Now we subtract 2625 from both sides:

`\begin{gathered} -15N=2100-2625 \\ -15N=-525 \end{gathered}`

Now we divide both sides by 15:

`N=-(525)/(-15)=35`

Now we replace this value in equation (2) where we already solved for W:

`\begin{gathered} W=75-35 \\ W=40 \end{gathered}`

Therefore, the time for the Wong family is 40 hours and the Nguyen family is 35 hours.