Solution:

The hare and the tortoise are together covering the distance at 11 miles per hour (i.e., on adding their speeds).
So, they will cover the distance of 44 miles in 4 hours.
Thus, in 4 hours, they will meet and the hare will have traveled 32 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 3 t miles.

Now,
8 t + 3 t = 44
So, t = 44 ⁄ 11 = 4 hours.

Thus, distance traveled by hare before meeting = 8 × 4 = 32 miles.

Food for thought:

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