A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is πr during the first 30 seconds, πr/2 during next one minute, πr/4 during next 2 minutes, πr/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?
Options:
A) 4  B) 8  C) 16  D) 32  E) 36
Explanation :   There is more than 1 way to approach the solution; however, I will detail the easiest way to go about it here.   We want to find the ratio of time taken for nth round : time taken for (n-1)th round   It will be same as finding the ratio of time taken for 2nd round : Time taken for 1st round.   1 round = Circumference of the circle = 2πr   1st round :   Speed = πr for 30 seconds. So, total distance travelled = πr/2.   Speed = πr/2 for 1 minute. So, total distance travelled = πr/2.   Speed = πr/4 for 2 minutes. So, total distance travelled = πr/2.   Speed = πr/8 for 4 minutes. So, total distance travelled = πr/2.   So, for a distance of 2πr, time taken is 7.5 minutes.   2nd round:   Speed = πr/16 for 8 minutes. So, total distance travelled = πr/2.   Speed = πr/32 for 16 minutes. So, total distance travelled = πr/2.   Speed = πr/64 for 32 minutes. So, total distance travelled = πr/2.   Speed = πr/128 for 64 minutes. So, total distance travelled = πr/2.   So, for a distance of 2πr, time taken is 120 minutes.   Ratio is 120:7.5 = 16:1.   Answer : 16
<result>C</result>
A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is πr during the first 30 seconds, πr/2 during next one minute, πr/4 during next 2 minutes, πr/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?