1971 AHSME Problems/Problem 34
Problem
An ordinary clock in a factory is running slow so that the minute hand passes the hour hand at the usual dial position(
o'clock, etc.)
but only every 
minutes. At time and one-half for overtime, the extra pay to which a 
per hour worker should be entitled
after working a normal 
hour day by that slow running clock, is
Solution
If the clock were functioning properly, the minute hand would have an angular velocity of 
, and the hour hand would have an angular velocity of 
. Thus, the minute hand would move at a velocity of 
relative to the hour hand. Thus, the minute hand would pass the hour hand every 
hours, or 
minutes (after the minute hand has made a full revolution relative to the hour hand). Because the slow clock takes minutes to do this, one hour to this clock is actually 
hours. Thus, hours on the slow clock is actually 
hours. Thus, the workers worked for an extra 
hours. Because, from the problem, the workers are paid 
times their usual wage when working overtime, they earn 
per hour in overtime. Therefore, they should receive 
extra dollars, so our answer is 
.
See Also
| 1971 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 33 |
Followed by Problem 35 | |
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| All AHSME Problems and Solutions | ||
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