Question

A sprinter starts running on a circular path of radius \(r\) metres. Her average speed (in metres/minute) is \( \pi \) during the first 30 seconds, \( \frac{\pi}{2} \) during next one minute, \( \frac{\pi}{4} \) during next 2 minutes, \( \frac{\pi}{8} \) during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?

• A. 4
• B. 8
• C. 16
• D. 32

Hint:

In problems involving decreasing speeds or times, check for geometric sequences and apply the ratio of successive terms.

Answer 1

The Correct Option is B

The time taken for each round decreases geometrically with the common ratio of 2. Since the average speed is inversely proportional to the time taken for each round, the ratio of time for the nth round to the previous round is 8. \[ \boxed{8} \]