A hare and a tortoise compete in a race over a straight course 1.55 km long. The tortoise crawls at a speed of 0.100 m/s toward the finish line. The hare runs at a speed of 7.85 m/s toward the finish line for 1.240 km and then stops to tease the slow-moving tortoise as the tortoise eventually passes by. The hare waits for a while after the tortoise passes and then runs toward the finish line again at 7.85 m/s. Both the hare and the tortoise cross the finish line at the exact same instant. Assume both animals, when moving, move steadily at their respective speeds. Required:
How far is the tortoise from the finish line when the hare resumes the race?

The tortoise is 3.95 m from the finish line when the hare resumes the race

Explanation:

Since, both the  tortoise and the rabbit continue with the same uniform speed. Therefore, we will use the equation for constant speed, that is:

s = vt

t = s/v

where,

s = distance covered

v = speed

t = time taken

Now, we consider the motion of tortoise:

t₁ = s₁/v₁

For hare:

t₂ = s₂/v₂

According to the given condition both hare and tortoise cross the finish line at same instant. Therefore, time for both must be equal.

t₁ = t₂

using values:

s₁/v₁ = s₂/v₂

where,

s₁ = distance of tortoise from finish line when hare starts = ?

v₁ = speed of tortoise = 0.1 m/s

s₂ = distance of hare from finish line when he starts = 1.55 km - 1.24 km = 0.31 km = 310 m

v₂ = speed of hare = 7.85 m/s

Therefore,

s₁/(0.1 m/s) = (310 m)/(7.85 m/s)

s₁ = (0.1 m/s)(39.5 s)

s₁ = 3.95 m

+15-35=-20

going in opposite directions