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 88 miles in 8 hours.
Thus, in 8 hours, they will meet and the hare will have traveled 80 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 10 t miles.
In t hours, the tortoise will travel 1 t miles.

Now,
10 t + 1 t = 88
So, t = 88 ⁄ 11 = 8 hours.

Thus, distance traveled by hare before meeting = 10 × 8 = 80 miles.

Food for thought:

Wish to try a more challenging puzzle similar in concept to this one? Then click here.