A tortoise can run with a speed of 10.1 cm/s, and a hare can run 19.4 times as fast. In a race, they both start at the same time, but the hare stops to rest for 122 seconds. The tortoise wins by a shell (20.8 cm).

Question

How long does the race take?

What is the length of the race?

Answer 1

tortoise= 10.1 t
hare= 195.94(t-122)

tortoise - hare= 10.1t - 195.94t + 23904.68 = 20.8

Solve for t

23883.88 = 185.84 t
t = 128.5185 s

tortoise t= (10.1)(128.5185)= 129.036 cm

Answer 2

A tortoise and a hare are having a 1.00km race. The tortoise runs the race at a constant speed of 2.30 cm/s. The hare moves at an average speed of 1.50 m/s for 10.0 minutes and then decides to take a nap. After waking up from the nap, the hare recognizes that the tortoise is about to cross the finish line and immediately accelerates from rest with a constant acceleration of 0.500 m/s2 for the remaining distance of the race. If the tortoise wins by a hair (pun intended), then what is the time (in hours) that the hare napped?