Systems of equations

Question

The Miller family and the Baker family each used their sprinklers last summer.The water output rate for the Miller family's sprinkler was 30 L per hour. The water output rate for the Baker family's sprinkler was 40L per hour. The families used their sprinklers for a combined total of 55 hours resulting in a water output of 1850 L. How long was each sprinkler used?

Answer 1

Miller:

 

x = duration of water use (hours)

(30 L per hour)*x = amount used

 

Baker:

 

y = duration of water use (hours)

(40 L per hour)*y = amount used

 

Total water usage: 1850 L = (30 L per hour)*x + (40 L per hour)*y

Total time of usage: x+y = 55 hours

 

This becomes a system of 2 linear equations in 2 unknowns x and y:

 

x + y = 55

30x + 40y = 1850

 

Get x = 55 - y from first equation, plug into second equation, and solve for y:

 

30(55-y) + 40y = 1850

1650 - 30y + 40y = 1850

10y = 200

y = 20

 

Plug y back into first equation and solve for x:

 

x = 55-y = 55-20 = 35

 

Miller ran the sprinkler for 35 hours and Baker ran them for 20 hours.