Question

A tortoise can run with a speed of 11.5 cm/s, and a hare can run 21.4 times as fast. In a race, they both start at the same time, but the hare stops to rest for 126 seconds. The tortoise wins by a shell (18.3 cm). How long does the race take? What is the length of the race?

Answer 1

if the race is over distance d cm, then at the end, the tortoise has gone d, and the hare has only gone d-18.3

If the tortoise goes at speed 11.5 cm/s, the hare runs at 21.4*11.5=246.1

Now, the hare's running time is 126 s less than the tortoise's.

Since the total times are equal, and time = distance/speed, we have

d/11.4 = (d-18.3)/246.1 + 126
d = 1507.06 cm

check:

1507.06/11.5 = 132.2 sec
1488.76/246.1 = 6.1 sec + 126 = 132.1