Runner walks on a circular track with a radius of 15m. What is the runner’s average speed in m/s if he walked halfway in 10 minutes. Answer in 2 decimal places.

The problem involves calculating the average speed of a runner walking halfway around a circular track with a radius of 15 meters in 10 minutes.

### Step 1: Find the total distance for half the circle
The circumference \( C \) of a circle is calculated using the formula:

\[
C = 2\pi r
\]

where \( r \) is the radius of the circle.

\[
C = 2\pi \times 15 = 30\pi \text{ meters}
\]

Halfway around the circle would be:

\[
\text{Halfway distance} = \frac{30\pi}{2} = 15\pi \text{ meters}
\]

Approximating \( \pi \approx 3.1416 \):

\[
\text{Halfway distance} \approx 15 \times 3.1416 = 47.12 \text{ meters}
\]

### Step 2: Convert time to seconds
The runner took 10 minutes to walk halfway around the track. To convert minutes to seconds:

\[
10 \text{ minutes} = 10 \times 60 = 600 \text{ seconds}
\]

### Step 3: Calculate average speed
The average speed \( v \) is given by the formula:

\[
v = \frac{\text{distance}}{\text{time}}
\]

Substituting the values:

\[
v = \frac{47.12}{600} \approx 0.0785 \text{ m/s}
\]

### Final Answer:
The runner’s average speed is approximately **0.08 m/s**.

Would you like any further clarification on this? Here are some related questions:

1. How do you calculate the full circumference of a circle?
2. What would be the runner's speed if they completed a full lap in 10 minutes?
3. How is average speed different from instantaneous speed?
4. What if the radius of the track was doubled? How would that affect the average speed?
5. How would the speed change if the time taken was reduced by half?

**Tip:** Always ensure the units are consistent when calculating speed—commonly meters per second (m/s).

Runner walks on a circular track with a radius of 15m. What is the runner’s average speed in m/s if he walked halfway in 10 minutes?

Learn how to calculate the average speed of a runner walking halfway around a circular track with a radius of 15m in 10 minutes. This problem involves using the formula for the circumference of a circle and basic speed calculation. The solution includes converting time to seconds and calculating distance using π. Suitable for students in Grades 6-8.

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