
The Bell family and the Campbell family each used their sprinklers last summer. The water output rate for the Bell family's sprinkler was 20 L per hour. The water output rate for the Campbell family's sprinkler was 30 L per hour. The families

used their sprinklers for a combined total of 60 hours, resulting in a total water output of 1600 L. How long was each sprinkler used?

Let \( x \) be the number of hours the Bell family used their sprinkler, and \( y \) be the number of hours the Campbell family used theirs. We have two main conditions to set up equations:

1. **Total time used**: The combined time both families used their sprinklers is 60 hours:
   \[
   x + y = 60
   \]

2. **Total water output**: The combined water output from both families is 1600 L:
   - The Bell family's sprinkler has an output rate of 20 L/hour, so they used \( 20x \) liters.
   - The Campbell family's sprinkler has an output rate of 30 L/hour, so they used \( 30y \) liters.
   - Thus, the total water output is:
   \[
   20x + 30y = 1600
   \]

### Solve the System of Equations:
We have the following system of equations:
\[
x + y = 60
\]
\[
20x + 30y = 1600
\]

**Step 1: Solve for \( y \) in terms of \( x \):**

From the first equation:
\[
y = 60 - x
\]

**Step 2: Substitute \( y \) into the second equation:**

\[
20x + 30(60 - x) = 1600
\]

Expand and simplify:
\[
20x + 1800 - 30x = 1600
\]
\[
-10x + 1800 = 1600
\]
\[
-10x = -200
\]
\[
x = 20
\]

**Step 3: Find \( y \):**

Substitute \( x = 20 \) into \( y = 60 - x \):
\[
y = 60 - 20 = 40
\]

### Solution:
- The Bell family used their sprinkler for **20 hours**.
- The Campbell family used their sprinkler for **40 hours**.

Would you like a detailed breakdown of any specific step? Here are some related questions to explore:

1. How would the solution change if the total output was 1800 L?
2. What if the Bell family's sprinkler output rate was increased to 25 L per hour?
3. How does changing the total hours used impact the outcome?
4. Can this problem be solved using matrices or graphing?
5. What are other examples of real-world problems that can be modeled by systems of equations?

**Tip:** When solving systems of equations, substitution is particularly useful if one of the equations can be easily solved for one variable.

The Bell family and the Campbell family each used their sprinklers last summer. The water output rate for the Bell family's sprinkler was 20 L per hour. The water output rate for the Campbell family's sprinkler was 30 L per hour. The families used their sprinklers for a combined total of 60 hours, resulting in a total water output of 1600 L. How long was each sprinkler used?

Learn how to solve a system of equations to find out how long each family used their sprinklers. The Bell family's sprinkler runs at 20 L/hour, and the Campbell family's at 30 L/hour. Together, they ran for 60 hours, using 1600 liters of water. Suitable for students in Grades 7-9.

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