SOLUTION: The Perez family and the Evans family each used their sprinklers last summer. The water output rate for the Perez family's sprinkler was 15L per hour. The water output rate for the

Question 1102739: The Perez family and the Evans family each used their sprinklers last summer. The water output rate for the Perez family's sprinkler was 15L per hour. The water output rate for the Evans family's sprinkler was 20L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1000L. How long was each sprinkler used?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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The Perez family and the Evans family each used their sprinklers last summer.
The water output rate for the Perez family's sprinkler was 15L per hour.
The water output rate for the Evans family's sprinkler was 20L per hour.
The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1000L.
How long was each sprinkler used?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

  x +   y =   55    (1)
15x + 20y = 1000    (2)


Express  x = 55 - y  from equation (1)   and substitute it into the equation (2). You will get

15*(55-y) + 20y =1000.


Simplify and solve it for y:

825 - 15y + 20y = 1000.

5y = 1000 - 825

5y = 175.

y =  = 35.


Then x = 55 - y = 55 - 35 = 20.


Answer. 20 hours of use by the Perez family, and 35 hours of use by the Evans family.

Check.  15*20 + 20*35 = 1000.   Correct !

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- The Robinson family and the Sanders family each used their sprinklers last summer
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