Puzzle 39

Thank you, Sam Loyd, for this one.
A sportive young hare and a tortoise raced in opposite directions around a circular track that was 100 yards in diameter. They started at the same spot, but the hare did not move until the tortoise had a start of one eighth of the distance (that is, the circumference of the circle). The hare held such a poor opinion of the other’s racing ability that he sauntered along, nibbling the grass until he met the tortoise. At this point the hare had gone one sixth of the distance.

How many times faster than he went before must the hare now run in order to win the race?

 

Answers saturday

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One Response to Puzzle 39

  1. James says:

    The diameter of the circular track has no bearing on the problem. When they meet, the hare has gone 1/6 of the way while the tortoise traveled 17/24. The tortoise has therefore been moving 17/4 times as fast as the hare. The hare has 5/6 of the distance yet to go as compared to 1/6 for the tortoise, so the hare must go five times faster than the tortoise, or 85/4 times faster than he went before.

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