algebra word problem

Question

The Chen family and the Torres family each used their sprinklers last summer. The Chen family's sprinkler was used for 15 hours. The Torres family's sprinkler was used for 20 hours. There was a combined total output of 900 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 50 L per hour?

Answer 1

The Chen family

Used 15 hours, C liters of water, rate per hour is C/15

The Torres family

Used 20 hours, T liters of water, rate per hour is T/20

C + T = 900

C/15 + T/20 = 50

Multiply the second equation by 60 to eliminate the fractions

4C + 3T = 3000

-4C - 4T = -3600 Multiply first equation by -4

-T = -600 Add down

T = 600 liters

C + 600 = 900

C = 300

Chen rate = 300/15 = 20 L per hour

Torres rate = 600/20 = 30 L per hour