The Chen family and the Davis family each used their sprinkles last summer. The water output rate for the Chen Family's sprinkler was 25 L per hour. The water output for the Davis family's sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1175 L. How long was each sprinkler used?

Question

The Chen family and the Davis family each used their sprinkles last summer. The water output rate for the Chen Family's sprinkler was 25 L per hour. The water output for the Davis family's sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1175 L. How long was each sprinkler used?

Answer 1

Let x be the number of hours the Chen family used their sprinkler.

The Chen family's sprinkler outputted 25x liters of water.
The Davis family sprinkler was then used for 55 - x hours.
The Davis family's sprinkler outputted 15(55-x) liters of water.
25x + 15(55-x) = 1175
25x + 825 - 15x = 1175
10x = 350
x = <<35=35>>35
The Chen family used their sprinkler for 35 hours.
The Davis family used their sprinkler for 55 - 35 = <<55-35=20>>20 hours. Answer: \boxed{20}.

Answer 2

Let's assume that the Chen family used their sprinkler for x hours and the Davis family used their sprinkler for y hours.

According to the information given, the water output rate for the Chen family's sprinkler was 25 L per hour, so the total water output from their sprinkler is 25x L.
Similarly, the water output rate for the Davis family's sprinkler was 15 L per hour, so the total water output from their sprinkler is 15y L.

We are told that the combined total water output from both sprinklers is 1175 L, so we can write the equation:
25x + 15y = 1175

We also know that the families used their sprinklers for a total of 55 hours, so we can write another equation:
x + y = 55

Now, we have a system of equations:
25x + 15y = 1175
x + y = 55

We can solve this system of equations using any method. Let's use substitution.

From the second equation, we can express x in terms of y:
x = 55 - y

Substituting this value of x into the first equation:
25(55 - y) + 15y = 1175
1375 - 25y + 15y = 1175
-10y = 1175 - 1375
-10y = -200
y = -200 / -10
y = 20

Substituting the value of y back into the second equation:
x + 20 = 55
x = 55 - 20
x = 35

Therefore, the Chen family used their sprinkler for 35 hours, and the Davis family used their sprinkler for 20 hours.