Problem:
Yesterday Han drove hour longer than Ian at an average speed miles per hour faster than Ian. Jan drove hours longer than Ian at an average speed miles per hour faster than Ian. Han drove miles more than Ian. How many more miles did Jan drive than Ian?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Suppose that Ian drove for hours at an average speed of miles per hour. Then he covered a distance of miles. The number of miles Han covered by driving miles per hour faster for additional hour is
Since Han drove miles more than Ian,
The number of miles Jan drove more than Ian is consequently
Represent the time traveled, average speed, and distance for Ian as length, width, and area, respectively, of a rectangle as shown. A similarly formed rectangle for Han would include an additional unit of length and units of width as compared to Ian's rectangle. Jan's rectangle would have an additional units of length and units of width as compared to Ian's rectangle.
Ian
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Han
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Jan
Given that Han's distance exceeds that of Ian by miles, and Jan's and rectangles are twice the size of Ian's and rectangles, respectively, it follows that Jan's distance exceeds that of Ian by
The problems on this page are the property of the MAA's American Mathematics Competitions