Question

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The Bailey family and the Harris family each used their sprinklers last summer. The water output rate for the Bailey family's sprinkler was 15 L per hour. The water output rate for the Harris family's sprinkler was 40 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1325
. How long was each sprinkler used?

Answer 1

Bailey family's sprinkler was used for 35 hours and Harris family's sprinkler was used for 20 hours.

Explanation:

Set up a system of equations.

Let be "b" the time Bailey family's sprinkler was used and "h" the time Harris family's sprinkler was used.

Then:

`\left \{ {{b+h=55} \atop {15b+40h= 1,325}} \right.`

You can use the Elimination method. Multiply the first equation by -15, then add both equations and solve for "h":

`\left \{ {{-15b-15h=-825} \atop {15b+40h= 1,325}} \right.\\.............................\\25h=500\\\\h=(500)/(25)\\\\h=20`

Substitute
`h=20` into an original equation and solve for "b":

`b+20=55\\\\b=55-20\\\\b=35`