Problem: a sprinter starts running on a circular path of radius r metres . her average speed ( in metres / minute ) is π r during the first 30 seconds , π r / 2 during next one minute , π r / 4 during next 2 minutes , π r / 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 ?
Rationale: 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 2 nd round : time taken for 1 st round . 1 round = circumference of the circle = 2 π r 1 st round : speed = π r for 30 seconds . so , total distance travelled = π r / 2 . speed = π r / 2 for 1 minute . so , total distance travelled = π r / 2 . speed = π r / 4 for 2 minutes . so , total distance travelled = π r / 2 . speed = π r / 8 for 4 minutes . so , total distance travelled = π r / 2 . so , for a distance of 2 π r , time taken is 7.5 minutes . 2 nd round : speed = π r / 16 for 8 minutes . so , total distance travelled = π r / 2 . speed = π r / 32 for 16 minutes . so , total distance travelled = π r / 2 . speed = π r / 64 for 32 minutes . so , total distance travelled = π r / 2 . speed = π r / 128 for 64 minutes . so , total distance travelled = π r / 2 . so , for a distance of 2 π r , time taken is 120 minutes . ratio is 120 : 7.5 = 16 : 1 . answer : c
annotated_formula: power(2, 4)