Question

Two racers start a race at the same moment and finish in a tie. Which of the following must be true?

• A. The racers speeds at the end of the race must have been exactly the same
• B. The racers had to have the same speed at some moment but not necessarily at exactly the same time
• C. At some point during the race the two racers were not tied
• D. The racers must have had the same speed at the exactly the same time at some point in the race

Answer 1

Answer: (D)

The racers must have had the same speed at the exactly

the same time at some point in the race

Answer 2

Let trajectories are f(t) and g(t)

since f(t) – g(t) = 0 has two roots 0 & T

so f '(t) – g '(t) = 0 must have at least one root in (0, T)