Need algebra help for solving a value mixture problem using a system of linear equations

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Two families each used their sprinklers last summer. Family #1's sprinkler was used 30 hrs.  The 2nd family's sprinkler was used 20 hrs.  Their was a combined total output of 1050 L of water.  What was the water output for each sprinkler if the sum of the two rates was 45 L per hour?

Nov 15th, 2015

family 1=600

family 2=450

form a simultaneous equation 20a+30b=1050

a+b=45

a=rate of family 1

b=rate of family 2 solve by elimination

Nov 15th, 2015

20(45-b)+30b=1050

900-20b+30b=1050

900+10b=1050

10b=150

b=15

a+b=45

a+15=45

a=30

Replacing a and b to our original equation gives an output of family 1 using 600L while family 2 using 450L

Nov 15th, 2015

I'm sorry I think I mislead you I need the water output rate of each sprinkler if the sum of the two rates was 45 L per hour

Nov 15th, 2015

it's ok. Our equation solved the rate of each sprinkler as well. Sprinkler of the family1 had a rate of 30L per hour while sprinkler of the family 2 did a rate of 15L per hour

Nov 15th, 2015

thanks got it

Nov 15th, 2015

you most welcome. Glad I could help.

Nov 15th, 2015

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Nov 15th, 2015
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Nov 15th, 2015
Oct 16th, 2017
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