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).