SOLUTION: The Young family and the Kim family each used their sprinklers last summer. The Young family's sprinkler was used for 40 hours. The Kim family's sprinkler was used for 25 hours. Th

Algebra ->  Equations -> SOLUTION: The Young family and the Kim family each used their sprinklers last summer. The Young family's sprinkler was used for 40 hours. The Kim family's sprinkler was used for 25 hours. Th      Log On


   

Question 1200740: The Young family and the Kim family each used their sprinklers last summer. The Young family's sprinkler was used for 40 hours. The Kim family's sprinkler was used for 25 hours. There was a combined total output of 2075L of water. What was the water output rate for each sprinkler if the sum of the two rates was 65L per hour?
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
The Young family and the Kim family each used their sprinklers last summer.
The Young family's sprinkler was used for 40 hours.
The Kim family's sprinkler was used for 25 hours.
There was a combined total output of 2075L of water.
What was the water output rate for each sprinkler if the sum of the two rates was 65L per hour?
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Let Y be the water output rate for Y family;
Let K be the water output rate for K family.

Write equations as you read the problem

     Y +   K =   65    (1)    (counting the output rates)    
   
   40Y + 25K = 2075    (2)    (counting total combined output)


To solve the system, from eq(1) exress K = 65 - Y and substitute it into eq(2)

    40Y + 25*(65-Y) = 2075.


Simplify and find Y 

    40Y - 25Y = 2075 - 25*65

        15Y   =    450

          Y   =    450/15 = 30.


ANSWER.  The output rate is 30 L/h for Y family and 65-30 = 35 L/h for K family.

Solved.



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This kind or similar come up every few weeks.
SPRINKERRATE%2ATIME=VOLUME
Time is in hours, and volume in liters. 
           RATE             TIME            VOLUME

YOUNG        r               40              (r)(40)

KIM         65-r             25            (65-r)(25)

TOTAL       65                               2075

Create the volume sum equation, and solve....