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

Explanation:

Let's use variables to represent the unknowns. Let x be the number of hours the Chen family used their sprinkler and y be the number of hours the Davis family used their sprinkler.

We have two equations based on the information given:

The water output for the Chen family: 25 L/hour * x hours = 25x L

The water output for the Davis family: 15 L/hour * y hours = 15y L

Since the total water output was 1175 L and the combined total hours of usage was 55 hours, we can write another equation:

x hours + y hours = 55

Now we can set up a system of equations:

25x + 15y = 1175

x + y = 55

Solving this system of equations will give us the values of x and y, which represent the hours each family used their sprinklers.

To solve the system of equations, we can use either substitution or elimination. Let's use elimination.

From equation 2, we have x + y = 55. We can rearrange it to get x = 55 - y.

Now, substitute the value of x in equation 1:

25(55 - y) + 15y = 1175

Simplify the equation:

1375 - 25y + 15y = 1175

Combine like terms:

-10y = -200

Now, solve for y:

y = 20

Now, find the value of x using equation 2:

x = 55 - 20

x = 35

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