Question

The Brown family and the Hernandez family each used their sprinklers last summer. The Brown family's sprinkler was used for 30hours. The Hernandez family's sprinkler was used for 35 hours. There was a combined total output of 1975 L of water. What was thewater output rate for each sprinkler if the sum of the two rates was 60 L per hour?х$?Brown family's sprinkler: UL per hourHernandez family's sprinkler: IL per hour

Answer 1

Given:

The number of hours the Brown family used the sprinkler = 30 hours.

The number of hours the Hernandez family used the sprinkler = 35 hours.

The combined total output of the water = 1975 L of water.

The sum of the two rates = 60 L per hour

Required:

We need to find the output rate for each sprinkler.

Explanation:

Let x be the output rate for the Brown family sprinkler.

Let y be the output rate for the Hernandez family sprinkler.

The sum of the two rates = 60 L per hour

$x+y=60$

$x=60-y$

The combined total output of the water = 1975 L of water.

$30x+35y=1975$

$Substitute\text{ }x=60-y\text{ in the equation.}$

$30(60-y)+35y=1975$

$(30\times60)-30y+35y=1975$

$1800+5y=1975$

Substract 1800 from both sides of the equation.

$1800+5y-1800=1975-1800$

$5y=175$

Divie nboth sides by 5.

$\frac{5y}{5}=\frac{175}{5}$$y=35L\text{ per hour,}$

$Substitue\text{ y=35 in th equation }x=60-y.$$x=60-35$$x=25L\text{ per hour}$

Fnal answer:

Brown family's sprinkler: 25L per hour

Hernandez family's sprinkler: 35L per hour