Problem:
Cassandra sets her watch to the correct time at noon. At the actual time of PM, she notices that her watch reads and seconds. Assuming that her watch loses time at a constant rate, what will be the actual time when her watch first reads PM?
Answer Choices:
A. PM and seconds
B. PM
C. PM
D. PM
E. PM
Solution:
When it is PM it is minutes after noon, but Cassandra's watch has recorded only minutes and seconds, that is, minutes. Thus when her watch has recorded minutes since noon, the actual number of minutes passed is
In particular, when her watch reads PM it has recorded minutes past noon, so the actual number of minutes past noon is
or hours and minutes. Therefore the actual time is PM.
The problems on this page are the property of the MAA's American Mathematics Competitions