Problem:
The clock in Sri's car, which is not accurate, gains time at a constant rate. One day as he begins shopping he notes that his car clock and his watch (which is accurate) both say noon. When he is done shopping, his watch says and his car clock says . Later that day, Sri loses his watch. He looks at his car clock and it says . What is the actual time?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The ratio of time as measured by Sri's car clock to actual time is = . Therefore when the clock shows that hours have passed since noon, only hours have actually passed, so the actual time is .
Gaining minutes every half hour is equivalent to gaining hour every hours. Hence when the car clock reads the actual time is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions