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The Walker family and the James family each used their sprinklers last summer. The water output rate for the Walker family’s sprinkler was 20L per hour. The water output rate for the James family’s sprinkler was 35L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 1300L. How long was each sprinkler used?Walker family’s sprinkler:James family’s sprinkler:

Respuesta :

we have

Walker family= 20 L/H

James family = 35 L/H

Total time= 50h

total water= 1300L

let's x be the time walker family use the sprinkler

let's y be the time James family use the sprinkler

then the total time is given by

First equation

[tex]x+y=50[/tex]

second equation

then the flow of water of is

Walker family = x*20

James Family = y*35

since the total flow is 1300L

then

[tex](x\ast20)+(y\ast35)=1300[/tex][tex]20x+35y=1300[/tex]

now with the 2 system equation we can solve x and y

[tex]x=50-y[/tex]

then

[tex]20(50-y)+35y=1300[/tex][tex]1000-20y+35y=1300[/tex][tex]15y=300[/tex][tex]y=\frac{300}{15}=20[/tex]

then

x+20=50

x=50-20=30

wich means

the walker family use the sprinkler for 30h

and

the James family use the sprinkler for 20h

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