Question

the ward family and the ross family each used their sprinklers last summer. the water output rate for the ward familys sprinkler was 20 l per hour. the water output rate for the ross familys sprinkler was 35 l per hour. the families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 1450 l. how long was each sprinkler used? ward familys sprinkler: hours ross familys sprinkler: hours

Explanation:

Step1: Define variables

Let \( x \) be the hours Ward's sprinkler was used, and \( y \) be the hours Ross's sprinkler was used.
We have two equations:

1. \( x + y = 50 \) (total hours)
2. \( 20x + 35y = 1450 \) (total water output)

Step2: Solve the first equation for \( x \)

From \( x + y = 50 \), we get \( x = 50 - y \).

Step3: Substitute \( x \) into the second equation

Substitute \( x = 50 - y \) into \( 20x + 35y = 1450 \):
\[

$$\begin{align*} 20(50 - y) + 35y &= 1450 \\ 1000 - 20y + 35y &= 1450 \\ 1000 + 15y &= 1450 \\ 15y &= 1450 - 1000 \\ 15y &= 450 \\ y &= \frac{450}{15} \\ y &= 30 \end{align*}$$

\]

Step4: Find \( x \)

Substitute \( y = 30 \) into \( x = 50 - y \):
\( x = 50 - 30 = 20 \)

Answer:

Ward family's sprinkler: 20 hours
Ross family's sprinkler: 30 hours