Questions: The Bell family and the Lewis family each used their sprinklers last summer. The water output rate for the Bell family's sprinkler was 20 L per hour. The water output rate for the Lewis family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 35 hours, resulting in a total water output of 800 L. How long was each sprinkler used? Bell family's sprinkler: hours Lewis family's sprinkler: hours

The Bell family and the Lewis family each used their sprinklers last summer. The water output rate for the Bell family's sprinkler was 20 L per hour. The water output rate for the Lewis family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 35 hours, resulting in a total water output of 800 L. How long was each sprinkler used?

Bell family's sprinkler: hours

Lewis family's sprinkler: hours

Transcript text: The Bell family and the Lewis family each used their sprinklers last summer. The water output rate for the Bell family's sprinkler was 20 L per hour. The water output rate for the Lewis family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 35 hours, resulting in a total water output of 800 L. How long was each sprinkler used? Bell family's sprinkler: $\square$ hours Lewis family's sprinkler: $\square$ hours

Solution

Solution Steps

Step 1: Set up the equations

Given that $R_1 = 20$ liters/hour, $R_2 = 25$ liters/hour, $T = 35$ hours, and $W = 800$ liters, we have two equations:

$t_1 + t_2 = T$
$R_1t_1 + R_2t_2 = W$

Step 2: Solve the system of equations

From equation 1, we express $t_2$ in terms of $T$ and $t_1$: $t_2 = T - t_1$. Substituting $t_2$ in equation 2 gives us $R_1t_1 + R_2(T - t_1) = W$. Solving for $t_1$, we find $t_1 = \frac{W - R_2T}{R_1 - R_2}$. Substituting the given values, we find $t_1 = 15$ hours and $t_2 = 20$ hours.