Question

A hare and a tortoise compete in a race over a straight course 2.10 km long. The tortoise crawls at a speed of 0.180 m/s toward the finish line. The hare runs at a speed of 8.70 m/s toward the finish line for 1.680 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 8.70 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.

(a) How far is the tortoise from the finish line when the hare resumes the race?

?m

(b) For how long in time was the hare stationary?

s?

Answer 1

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

A hare and a tortoise compete in a race over a straight course 1.20 km long. The tortoise crawls at a speed of 0.140 m/s toward the finish line. The hare runs at a speed of 8.60 m/s toward the finish line for 0.960 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 8.60 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.

(a) How far is the tortoise from the finish line when the hare resumes the race?
m

(b) For how long in time was the hare stationary?   

Speed of tortoise = 0.140 m/s
Length of course =1.2 kms =1200 m

Total time taken by tortoise = Distance/ Speed = 1200/0.14 = 8571.43 seconds .

Initial distance covered by hare = 0.960 kms = 960 m
Speed of hare =8.60 m/s
Time take by hare for covering 960 m = 960//8.6 = 111.63 seconds.

The tortoise passes the hare after time t = 960/0.140 = 6857.143 seconds
Time needed need by hare to finish the last 240 m of race = 240/8.6 =27.91 seconds
Time needed by tortoise for the last 240 m of race = 240/0.14 = 1714.29 seconds.


Since both the hare and tortoise finished the race at the same time, therefore the Hare was resting for a time of (1714.29 -27.91) seconds

The hare was stationary for a time of t=1714.29-27.91 = 1686.38 seconds
The Tortoise was at a distance of d= 0.140 x 27.91 =3.91 metre from the finish line when the hare resumed the race.