Question

The Thompson family and the Kim family each used their sprinklers last summer. The Thompson family's sprinkler was used for 25 hours. The Kim family'ssprinkler was used for 35 hours. There was a combined total output of 1075 L of water. What was the water output rate for each sprinkler if the sum of the tworates was 35 L per hour?Thompson family's sprinkler:Kim family's sprinkler:

Answer 1

The water output rate for the Thompson family's sprinkler is 15 liters per hour, and the Kim family's sprinkler is 20 liters per hour, calculated using a system of linear equations.

Step-by-step explanation:

The student is trying to determine the water output rate for two family sprinklers based on the total usage and a combined rate. To solve this, we can set up a system of linear equations. Let's define T as the rate of the Thompson family's sprinkler in liters per hour and K as the rate of the Kim family's sprinkler, also in liters per hour.

We are given that T + K = 35 liters per hour and that the Thompson's sprinkler has been used for 25 hours and the Kim's for 35 hours, resulting in a combined total of 1075 liters. Thus, we have the equations:

1. 25T + 35K = 1075
2. T + K = 35

From the second equation, we can express T as T = 35 - K. Substituting this into the first equation:

25(35 - K) + 35K = 1075

Solving for K, we find that:

875 - 25K + 35K = 1075

10K = 200

K = 20 liters per hour

Thus, T = 35 - K = 35 - 20 = 15 liters per hour.

Therefore, the Thompson family's sprinkler has a rate of 15 liters per hour and the Kim family's sprinkler has a rate of 20 liters per hour.

Answer 2

Let x be the rate of water output by the Thompson family and let y be the rate of water output by the Kim family.

We know that the Thompson family sprinkler was used for 25 hours, Kim's family sprinkler was used for 35 hours and that there was a combined total output of 1075 L of water; then we have the equation:

`25x+35y=1075`

We also know that the combined water output was 35 L per hour, then:

`x+y=35`

Hence we have the system of equations:

`\begin{gathered} 25x+35y=1075 \\ x+y=35 \end{gathered}`

To solve this system we solve the second equation for y:

`\begin{gathered} x+y=35 \\ y=35-x \end{gathered}`

And we plug this value in the first equation and solve for x:

`\begin{gathered} 25x+35(35-x)=1075 \\ 25x+1225-35x=1075 \\ -10x=1075-1225 \\ -10x=-150 \\ x=(-150)/(-10) \\ x=15 \end{gathered}`

Once we have the value of x we plug it in the expression of y:

`\begin{gathered} y=35-15 \\ y=20 \end{gathered}`

Therefore we have that:

`\begin{gathered} x=15 \\ y=20 \end{gathered}`

which means:

Thompson family's sprinkler: 15 L per hour

Kim family's sprinkler: 20 L per hour.