Solution:

The hare and the tortoise are together covering the distance at 8 miles per hour (i.e., on adding their speeds).
So, they will cover the distance of 40 miles in 5 hours.
Thus, in 5 hours, they will meet and the hare will have traveled 35 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 7 t miles.
In t hours, the tortoise will travel 1 t miles.

Now,
7 t + 1 t = 40
So, t = 40 ⁄ 8 = 5 hours.

Thus, distance traveled by hare before meeting = 7 × 5 = 35 miles.

Food for thought:

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