RV Singh fights the law

Calculus Level 2

RV Singh needs to train for his next big race. Sadly, he doesn't have enough money to rent a racetrack, so he drives his car on the highway, which has a speed limit of 100 km per hr. The police are very mad at RV but they can't ever catch him speeding. Instead, the cops observe that RV enters the highway at 8:00 and exits the highway thirteen minutes later in a town 22 km away.

In court, RV points out, correctly, that the police never measured him going faster than 100 km per hr, and so, can't prove that he ever broke the speed limit. What should the judge decide?

The police must measure his speed to know for sure RV must have broken the speed limit RV could not have broken the speed limit Only RV knows if he broke the speed limit

Josh Silverman by Josh Silverman

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2 solutions

Himanshu Arora
Jul 16, 2014

As is given in the #tag section, this question is a direct application of Mean Value Theorem. The average speed is 101.54. So RV must have attained this or higher speeds during his journey at least once.

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Correct use of MVT

Rajat Dwivedi - 6 years, 11 months ago

i want some more explanation.

KRISHANG SACHDE - 6 years, 10 months ago

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Krishang, basically, you calculate the mean speed which RV reached during his drive. So that's approximately 101km/h. Note however, that RV says that the police don't measure his speed as above 100. This means that at a certain point in the journey, when the police took his speed reading, he was going below 100. But if he was, and the average speed is 101, then at some other instant of the journey, when the police weren't looking, RV was above 100. This reasoning is so because of the way we take a mean value, how larger or smaller values can alter the mean to the number we want. Hence, RV had to be over the speed limit at some point in the journey. I hope this helps, a bit long winded, but hope it helps. Cheers!

Kevin Mano - 6 years, 10 months ago
Michael Lucas
Oct 28, 2018

22km in0.217h is approx 101km/hr avg so he had to at som point exceeded 100km/hr. Mean value theorem

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