Question

The Chang family and the Davis family each used their sprinklers last summer. The water output rate for the Chang family's sprinkler was 15 L per hour. The water output rate for the Davis family's sprinkler was 40 L per hour. The families used their sprinklers for a combined total of 60 hours, resulting in a total water output of 1775 L. How long was each sprinkler used?

Answer 1

The Chang family = 25 hours, The Davis family = 35 hours

Explanation:

The given information is as follow

The Chang family = 15L/h

The Davis family = 40L/h

Total time for both sprinklers = 60 hours

Total water output = 1775 L

From this information we can derive a set of simultaneous equations to help us find our answer.

We need to find the following information

The time for the Chang family, taken as t1

The time for the Davis family, taken as t2

From this we derive the following set of equations

1) t1 + t2 = 60 hours ----- (This is derived from the total time for both sprinklers)

2) 15(t1) + 40(t2) = 1775 ---- (This is derived from total water output based on time for each sprinkler)

Solving these simultaneously we get following equation

t1 = 60 - t2 - equation 1

15(t1) + 40(t2) = 1775 - equation 2

15 (60 - t2) + 40(t2) = 1775 - equation 3 (combining equation 1 & equation 2)

900 - 15(t2) + 40(t2) = 1775 -------- solving the equation 3

25(t2) = 1775 - 900

t2 = 35

t1 = 25