EXAMPLE 3.7.9

Plato and Aristotle are loitering on the street corner, when suddenly Socrates (to whom they owe money) shows up. Plato takes off running eastward at a rate of 16 miles per hour, and Aristotle runs southward at a rate of 12 miles per hour. How far apart (direct distance) are Plato and Aristotle after 15 minutes?

SOLUTION

15 minutes is the same as 15/60 or 1/4 of an hour. After 1/4 of an hour, Plato will have run (1/4 hour) times (16 miles per hour) = 4 miles; Aristotle will have run (1/4 hour) times (12 miles per hour) = 3 miles. The diagram below shows the situation at that time.

The distance (D) between Plato and Aristotle is the hypotenuse of a right triangle whose legs measure 3 miles and 4 miles, respectively. According to the Pythagorean Theorem,

D squared equals 4 squared plus 3 squared
D squared equals 16 squared plus 9
D squared equals 25
D equals the square root of 25
The square root of 19,200 equals D.
D equals 5 miles.