SOLUTION: Please help The Johnson family and the Nguyen family each used their sprinklers last summer. The Johnson family's sprinkler was used for 25 hours. The Nguyen family's sprinkler

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Question 1171644: Please help
The Johnson family and the Nguyen family each used their sprinklers last summer. The Johnson family's sprinkler was used for 25 hours. The Nguyen family's sprinkler was used for 35 hours. There was a combined total output of 1025 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 35 L per hour?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
rate * time = quantity

let n = the rate of the nguyen family.
let j = the rate of the johnson family.

your equation becomes:
35 * n + 25 * j = 1025

this equation means that the rate of the nguyen family * 35 hours plus the rate of the johnson family * 25 hours equals a total output of 1025 liters of water.

you are given that n + j = 35 liters of water per hour.
solve for n to get n = 35 - j.

the equation of 35 * n + 25 * j = 1025 becomes:
35 * (35 - j) + 25 * j = 1025.
simplify to get:
1225 - 35 * j + 25 * j = 1025
combine like terms to get:
1225 - 10 * j = 1025
subtract 1025 from both sides of the equation and add 10 * j to both sides of the equation to get:
1225 - 1025 = 10 * j.
combine like terms to get:
200 = 10 * j
solve for j to get:
j = 20
since n + j = 35, then n = 15.
you have:
n = 15
j = 20
replace n and j in the original equation with these values to get:
35 * n + 25 * j = 1025 becomes:
35 * 15 + 25 * 20 = 1025 which becomes:
525 + 500 = 1025 which becomes:
1025 = 1025
this confirms the values are good.
your solution is that the water sprinkler rate for the nguyen family was 15 liters per hours and the water sprinkler rate for the johnson family was 20 liters per hour.