Question

The Thomas family and the Clark family each used their sprinklers last summer. The water output rate for the Thomas family's sprinkler was 35L per hour. The water output rate for the Clark family's sprinkler was 15L per hour. The families used their sprinklers for a combined total of 40 hours, resulting in a total water output of 1100L. How long was each sprinkler used?

Answer 1

Answer:

x  =  15  hours  

y  =  25  hours

Step-by-step explanation:

Lets call  "x"  number of working hours of Clark family sprinklers

and   " y "  number of working hours of Thomas family sprinklers

Then they both worked in such way that

x  +  y  =  40   (1)

On the other hand the total water output  1100 lts were supplied according to:

35 lts/h *  y (hours)   +  15 lts/h *  x (hours)  =  1100 lts

Then  

35*y   +  15*x  =  1100   (2)

Equations 1 and 2 become a system of two equations with two uknown variables  x  and  y

We solve that system

y   =  40  -  x        and     35* ( 40 - x ) +  15* x    =  1100

1400  -  35x   +  15x   = 1100    ⇒    -  20x  = -300

x  =  15  hours

And

y  =  40  -  15   =  25  hours