Time difference on circle — It takes 30 s less along the diameter than around the boundary at speed 30 m/min. Find the circle radius (π = 22/7).

Introduction / Context:
The walker compares two routes across a circle: the circumference 2πr and the straight diameter 2r. The difference in times at the same speed equals the difference in distances divided by that speed, allowing us to solve for r.

Given Data / Assumptions:

• Speed v = 30 m/min
• Time difference Δt = 30 s = 0.5 min
• Distance difference Δd = 2πr − 2r = 2r(π − 1)
• π = 22/7

Concept / Approach:
Use v = distance / time ⇒ Δd = v * Δt. Equate 2r(π − 1) with vΔt and solve for r.

Step-by-Step Solution:
Δd = 30 * 0.5 = 15 m2r(π − 1) = 15 ⇒ 2r((22/7) − 1) = 15 ⇒ 2r(15/7) = 15(30/7)r = 15 ⇒ r = 15 * 7 / 30 = 3.5 m

Verification / Alternative check:
Compute distances: circumference ≈ 2 * (22/7) * 3.5 = 22 m; diameter = 7 m; difference = 15 m. Time at 30 m/min: 0.5 min ✔

Why Other Options Are Wrong:
All other radii give a different difference than 15 m when plugged into 2r(π − 1).

Common Pitfalls:
Using 30 s as 30 min or 0.3 min; forgetting that both routes are through the same circle center.

Final Answer:
3.5 m