Hare in the other. The hare starts after the tortoise has covered 1/3 ...
Understanding the scenario:
The tortoise and the hare are racing along a circle with a diameter of 100 yards. The tortoise starts first and moves at a constant speed. The hare starts later and moves leisurely until it covers 1/3 of its distance.
Meeting point:
The hare and tortoise meet when the hare has covered only 1/8 of the distance. This means that the hare covers 1/8 of the circle's circumference by the time they meet.
Calculating distances:
The tortoise covers 1/3 of the circle's circumference before they meet, which is 1/3 * 2 * π * 50 = 100π/3 yards. The hare covers 1/8 of the circle's circumference when they meet, which is 1/8 * 2 * π * 50 = 25π yards.
Speed ratio:
To tie the race, the hare needs to cover the remaining distance in the same time it took to cover the initial 1/8. The hare should increase its speed by a factor that is the ratio of the remaining distance to the distance covered initially. This ratio is (100 - 25)π / (100 - 25π) = 75π / (100 - 25π) ≈ 30.33.
Therefore, the hare should increase its speed by a factor of approximately 30.33 to tie the race. The correct answer is option 'A'.
Hare in the other. The hare starts after the tortoise has covered 1/3 ...
1/3, 1/8
3*8=24
(24-3)=21
(21-8)=13
(21*13)/3^2