Problem:
Andy and Betsy both live in Mathville. Andy leaves Mathville on his bicycle at , traveling due north at a steady miles per hour. Betsy leaves on her bicycle from the same point at , traveling due east at a steady miles per hour. At what time will they be exactly the same distance from their common starting point?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the number of hours after . Then, if we represent Andy's distance as and Betsy's distance as , we get
Thus, for these to be equal, we set , so , or . This means that they reach this equidistant point hours after , or at .
The problems on this page are the property of the MAA's American Mathematics Competitions