you need eight barrels of water to sprinkle 1/2 mile of roadway. How many barrels of water do you need to sprinkle 3 1/2 miles of roadway? Please solve and explain.

To solve this problem, we can use a ratio approach. We know the following:

- **8 barrels** of water are needed to sprinkle **1/2 mile** of roadway.
- We are asked how many barrels of water are needed to sprinkle **3 1/2 miles** of roadway.

### Step 1: Set up the ratio
Since 8 barrels are used for 1/2 mile, we can find the number of barrels per mile by scaling this proportionally.

- For 1 mile of roadway, the number of barrels needed is:

\[
\text{Barrels per mile} = \frac{8 \text{ barrels}}{\frac{1}{2} \text{ mile}} = 8 \times 2 = 16 \text{ barrels per mile}.
\]

### Step 2: Multiply by the total miles
Now that we know it takes 16 barrels per mile, we can multiply this by the 3 1/2 miles (or \( \frac{7}{2} \) miles) of roadway:

\[
\text{Total barrels} = 16 \times \frac{7}{2} = 16 \times 3.5 = 56 \text{ barrels}.
\]

### Final Answer:
You need **56 barrels of water** to sprinkle 3 1/2 miles of roadway.

---

Would you like more details or have any questions?

Here are some related questions to explore:

1. How many barrels would be needed for 1 mile of roadway?
2. If only 10 barrels were available, how much roadway could be sprinkled?
3. What would happen if the requirement increased to 10 barrels per 1/2 mile?
4. How many barrels would be needed for 5 miles of roadway?
5. If you had only 30 barrels, what fraction of 3 1/2 miles could be sprinkled?

**Tip:** Ratios are a powerful tool for scaling problems up or down proportionally.

Discover how to calculate the number of barrels of water needed to sprinkle 3 1/2 miles of roadway using ratios and proportional reasoning. This problem is suitable for students in Grades 6-8 and includes a step-by-step explanation of the solution.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation