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
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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):
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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?
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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 !
