Question

The Tanaka family and the Butler family each used their sprinklers last summer. The water output rate for the Tanaka family’s sprinkler was 20L per hour. The water output rate for the Butler family’s sprinkler was 40L per hour. The families used their sprinklers for a combined total of 45 hours, resulting in a total water output of 1200L. How long was each sprinkler used?

a) Tanaka family's sprinkler: 25 hours, Butler family's sprinkler: 20 hours
b) Tanaka family's sprinkler: 15 hours, Butler family's sprinkler: 30 hours
c) Tanaka family's sprinkler: 30 hours, Butler family's sprinkler: 15 hours
d) Tanaka family's sprinkler: 20 hours, Butler family's sprinkler: 25 hours

Answer 1

After setting up two equations based on the given water output rates and solving for the two unknowns, we find that the Tanaka family's sprinkler was used for 30 hours and the Butler family's sprinkler was used for 15 hours, which correlates to option c.

Step-by-step explanation:

The question involves determining the duration each family used their sprinkler given the water output rates and the total usage in hours and liters. We are given that the Tanaka family's sprinkler has a rate of 20L per hour and the Butler family's sprinkler has a rate of 40L per hour. The total use is 45 hours resulting in 1200L of water output.

Let's denote the time the Tanaka family used their sprinkler as T hours and the Butler family as B hours. The combined hours of usage is:

T + B = 45

The total water output from both families is:

20L/h × T + 40L/h × B = 1200L

Now we have a system of two equations with two unknowns:

1. T + B = 45
2. 20T + 40B = 1200

To solve the system, we can multiply the first equation by 20 to help eliminate a variable:

1. 20T + 20B = 900
2. 20T + 40B = 1200

Subtracting the first equation from the second gives us:

20B = 300 → B = 15

Substituting B = 15 into the first equation:

T + 15 = 45 → T = 30

Therefore, the Tanaka family used their sprinkler for 30 hours, and the Butler family used their sprinkler for 15 hours, which corresponds to option c in the original question.