Each spring a hare challenges a tortoise to a 50 m race. The hare knows that he can run faster than the tortoise, and he boasts that he can still win the race even if he gives the tortoise a 100 s head start. The tortoise crawls at a rate of 0.4 m/s, and the hare's running speed is 1.8 m/s.
a. Write equations to simulate the motion of the tortoise.
b. Determine a graphing window and a range of t-values that will show the tortoise's motion.
c. Write equations to simulate the motion of the hare, who crosses the starting line at t = 100.
d. Who wins the race?
e. How long does it take each runner to finish the race?