Question

A hare
and a turtle
decided to race each other, the race beginning at an oak tree and
finishing at a pine tree. The turtle's speed was only half of that of the hare. However, the
hare got caught cheating and was forced to hop back to the oak tree and start again, after it
had already covered 2/3rd of the total distance. The turtle, slow but steady and honest, won
the race by 8 minutes. How long did the hare take to complete the race?​

Answer 1

Solution :-

Given that, The turtle's speed was only half of that of the hare.

So,

Let us assume that, the speed of hare is x km/min .

Than, speed of turtle will be = (x/2) km/min.

Let us also assume that, total distance from the oak tree to the pine tree is d km.

Now, we have given that, after covering 2/3rd of the total distance , the hare caught cheating and send back to starting point again .

So,

→ Distance after hare caught cheating = (2/3)rd of total distance = (2/3) of d = (2d/3) km.

Therefore,

→ Total distance covered by the hare = (2d/3)(front) + (2d/3)(Back) + again Total distance = (2d/3) + (2d/3) + d = (7d/3)

Hence,

→ Time taken by hare to complete the race = (Total distance covered) / (Speed) = {(7d/3)} / (x) = (7d/3x) Min.

Also,

→ Time taken by turtle to complete the race = (Total distance covered) / (Speed) = d / (x/2) = (2d/x) Min.

Now, it is given that, the turtle beat the hare by 8 minutes.

So,

→ Time taken by the hare to complete the race - Time taken by the turtle to complete the race = 8

→ (7d/3x) - (2d/x) = 8

→ (7d - 6d)/3x = 8

→ (d/3x) = 8

→ (d/x) = 8 * 3

→ (d/x) = 24 Min.

Hence,

→ Time taken by hare to complete the race = (7d/3x) = (7/3) * (d/x) = (7/3) * 24 = 56 Min. (Ans.)