Question

The Russell family and the Wright family each used their sprinklers last summer. The Russell family's sprinkler was used for 25 hours. The Wright family's sprinkler was used for 30 hours. There was a combined total output of 1700L of water. What was the water output rate for each sprinkler if the sum of the two rates was 60L per hour?

Answer 1

Let v_R and v_W be Rusells' and Wrigths' sprinkler water output rates, respectively.

Therefore,

`\begin{gathered} 25\cdot v_R+30\cdot v_W=1700_{} \\ \text{and} \\ v_R+v_W=60 \end{gathered}`

Where v_R and v_W are given in liters per hour.

The equations above are provided by the question. Solve the system of equations as shown below

`\begin{gathered} v_R+v_W=60\Rightarrow v_R=60-v_W \\ \Rightarrow25(60-v_W)+30\cdot v_W=1700 \\ \Rightarrow1500-25v_W+30v_W=1700 \\ \Rightarrow5v_W=200 \\ \Rightarrow v_W=40 \end{gathered}`

And,

`\begin{gathered} v_W=40 \\ \Rightarrow v_R+40=60 \\ \Rightarrow v_R=20 \end{gathered}`

Therefore, the water output rate of the Russell family's sprinkler is 20 liters per hour while the water output rate of the Wright family's sprinkler is 40 liters per hour