Let's solve this step by step.
Problem:
You run 5 miles in 40 minutes. Your friend runs 8 miles at the
same pace as you. How long does it take your friend to run 8 miles?
---
Step 1: Understand the situation
Since both you and your friend run at the
same pace, we can set up a
proportion based on distance and time.
We know:
- You run
5 miles in 40 minutes
- Your friend runs
8 miles in $ x $ minutes (unknown)
We want to find $ x $, the time it takes your friend to run 8 miles.
---
Step 2: Set up the proportion
We write the ratio of distance to time for both runs:
$$
\frac{5 \text{ miles}}{40 \text{ minutes}} = \frac{8 \text{ miles}}{x \text{ minutes}}
$$
This is a proportion because the
pace (miles per minute) is the same.
---
Step 3: Solve the proportion
Cross-multiply:
$$
5x = 40 \times 8
$$
$$
5x = 320
$$
Now divide both sides by 5:
$$
x = \frac{320}{5} = 64
$$
---
Answer:
Your friend’s run takes
64 minutes.
---
✔ Final Answer:
64 minutes
---
Explanation:
Since the pace is constant, the ratio of distance to time stays the same. By setting up a proportion and solving, we found that running 8 miles at the same pace as 5 miles in 40 minutes takes 64 minutes.
Parent Tip: Review the logic above to help your child master the concept of proportion problems.
