The harris family and the carter family each used their sprinklers last summer. The water output rate for the Harris family's sprinkler was 25 L per hour. The water output rate for the Carter family's sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1075 L. How long was each sprinkler used?

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NoriannaD498230 NoriannaD498230 · Answer 1 · 2022-11-03T17:20:46+01:00

Let Harris family used their sprinkler for x hours and Carter family used their sprinkler for y hours.

Then the equation for total time of sprinkler use is,

[tex]\begin{gathered} x+y=55 \\ y=55-x \end{gathered}[/tex]

Determine the equation for total water output from both the sprinkler.

[tex]\begin{gathered} 25x+15y=1075 \\ 5x+3y=215 \end{gathered}[/tex]

Substitute 55-x for y in the equation to eliminate the y terms.

[tex]\begin{gathered} 5x+3(55-x)=215 \\ 5x+165-3x=215 \\ 2x=50 \\ x=25 \end{gathered}[/tex]

Substitute 25 for x in the equation y=55-x to obtain the value of y.

[tex]\begin{gathered} y=55-25 \\ =30 \end{gathered}[/tex]

So Harris family used sprinkler for 25 hours and Carter family used sprinkler for 30 hours.