Question

Mike and Mitchell decide to have a foot race. They mark off a stretch of 100 yards, and recruit Cindy to work the stopwatch. Mike took less time than Mitchell to run the 100 yards, what does this tell us about his speed? A) That Mike is faster than Mitchell. B) That Mike is slower than Mitchell. C) That Mitchell is faster than Mike. D) Without knowing the exact times, you can't say for sure.

Answer 1

The correct answer is
A) That Mike is faster than Mitchell.

In fact, Mike took less time than Mitchell to cover the 100 yards. If we call S=100 y the distance covered by Mitchell and Mike, and $t_{mike}$ the time Mike takes to cover this distance, Mike's average velocity can be written as
$v_{mike} = \frac{S}{t_{mike} }$
Similarly, Mitchell's average velocity is
$v_{mitchell} = \frac{S}{t_{mitchell}}$

The problem says that Mike took less time than Mitchell to cover the 100 yards, this means that $t_{mike} \ \textless \ t_{mitchell}$, and since the distance S is the same, by comparing the two formulas we can conclude that 
$v_{mike} \ \textgreater \ v_{mitchell}$
so, Mike is faster than Mitchell.