A hare and a tortoise competed in a 5 km race along a straight line. The hare is five times faster than the tortoise. The hare mistakenly started perpendicular to the route. After a while he realized his mistake, then turned and ran straight to the finish point. He arrived at the same time as the tortoise. What is the distance (in km) between the hare's turning point and the finish point?
Answers
Answer:
The answer is 40
Step-by-step explanation:
For hare and tortoise speed is given. Tortoise will take 12 hours to complete 1 round. And during this, hare will make 12 rounds of OP.
In the first round, both has started from point O. After some time, hare will cross tortoise and distance between them will be 1 km. After some more time, when hare is returning back from P to O, before and after crossing tortoise, hare will be two more times 1km apart from tortoise. So, in first round, there are three such occurrences.
In the second round, when hare has started from point O, while going and returning back, there will be four occurrences when before and after crossing the tortoise, hare will be eactly 1 km apart. But the first occurance of round 2 is already counted in round 1. So, in second round as well, there will be total 3 occurrences.
In the third, fourth and fifth rounds, there will be 4 such occurrences.
In the sixth round, because tortoise will be at point P, there will be only 2 cases.
Now, till round 6 there are 20 such occurrences. And from round 7 to 12, it will exactly same but in reverse order. Hence, total such occurrences = 20 * 2 = 40.
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