Problem:
Josh and Mike live miles apart. Yesterday Josh started to ride his bicycle toward Mike's house. A little later Mike started to ride his bicycle toward Josh's house. When they met, Josh had ridden for twice the length of time as Mike and at four-fifths of Mike's rate. How many miles had Mike ridden when they met?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because (rate) time distance , the distance Josh rode was of the distance that Mike rode. Let be the number of miles that Mike had ridden when they met. Then the number of miles between their houses is
Thus .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions