SOLUTION: The Adams family and the Evans family each used their sprinklers last summer. The Adams family sprinkler was used for 40 hours. The Evans family sprinkler was used for 25 hours. Th

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Question 1051248: The Adams family and the Evans family each used their sprinklers last summer. The Adams family sprinkler was used for 40 hours. The Evans family sprinkler was used for 25 hours. There was a combined total output of 1350 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 45 L per hour?
Answer by Theo(13342) About Me  (Show Source):
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let x = the liters per hour for the adams family.
let y = the liters per hour for the evans family.

the sum of the combined rates is 45 liters per hour.

that means that x + y = 45

the total output is 1350 liters.
the adams family sprinkled for 40 hours.
the evans family sprinkled for 25 hours.

rate * time = quantity.

this means that 40x + 25y = 1350.

40x is the number of liters that the adams family used.
25y is the number of liters that the evans family used.

you have two equations that need to be solved simultaneously.

they are:

x + y = 45
45x + 25y = 1350

solve for y in the first equation to get y = 45 - x.

replace y with 45 - x in the second equation to get 45x + 25(45-x) = 1350

simplify to get 45x + 1125 - 25x = 1350

combine like terms to get 15x = 225

solve for x to get x = 15

since x + y = 45, then y must be equal to 30.

you get x + y = 15 + 30 = 45.

you get 40*15 + 25*30 = 600 + 750 = 1350.

the formula check out so the solution looks good.

the adams family sprinkled 40 hours at 15 liters per hour for a total of 600 liters.

the evans family sprinkled 25 hours at 30 liters per hour for a total of 750 liters.

the total number of liters sprinkled was 600 + 750 = 1350 liters total.