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The Hare and the Tortoise

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Haretown and Tortoiseville are 30 miles apart. A hare travels at 8 miles per hour from Haretown to Tortoiseville, while a tortoise travels at 2 miles per hour from Tortoiseville to Haretown.

If both set out at the same time, how many miles will the hare have to travel before meeting the tortoise en route?

Answer: 24


The hare and the tortoise are together covering the distance at 10 miles per hour (i.e., on adding their speeds).
So, they will cover the distance of 30 miles in 3 hours.
Thus, in 3 hours, they will meet and the hare will have traveled 24 miles.

Alternative Solution through Equations:

Note that : Distance = Speed × Time

Let t be the time before the hare and the tortoise meet.
In t hours, the hare will travel 8 t miles.
In t hours, the tortoise will travel 2 t miles.

8 t + 2 t = 30
So, t = 30 ⁄ 10 = 3 hours.

Thus, distance traveled by hare before meeting = 8 × 3 = 24 miles.

Food for thought:

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