Expert: Steve Holleran - 10/23/2007

Question
1. Suppose that in a race, horse A and horse B begin at the same point and finish in a dead heat. Prove that their speeds were identical at some instant of the race.

2. John traveled 112 miles in 2 hours and claimed that he never exceeded 55mph. Use the Mean Value Theorem to disprove his claim.

Thank you for all your help!

Answer
Hi Alex,

1.  Well, I don't know what type of "proof" is needed here, but if they covered the same distance in the same time, then their average velocities were equal (just using d=rt).

Then, according to the MVT, their instantaneous velocities had to be the same on the closed interval at least once.

2.  Okay, John's average velocity here is 112 mi / 2 hr
   = 56 mi/hr.  According to the MVT, his instantaneous velocity must have been 56 at least once, also.

Hope this is okay.

Steve