Home Maths Differentiation and Applications of Derivatives General Two racers start a race at the same moment a…
Maths Differentiation and Applications of Derivatives General Single Correct MCQ
Published on: August 13, 2026

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

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Verified by Experts
The correct answer is:
D

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)

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