A clock tower has a bell that rings out every hour of the day. (3 chimes at 3 o'clock P.M., etc.) These hourly tolls are spaced 1.5 seconds apart. The clock also chimes once at each half hour.

What is the overall average number of minutes between chimes?

first, I assume the chimes themselve are instantaneous.  Then, for each hour H (1 thru 12), there are
H-1 intervals of 1.5 seconds corresponding to intervals between hourly chimes
1 interval of 30*60-1.5*(H-1) corresponding to the interval between the last hourly chime and the half-hour chime
1 interval of 30*60 corresponding to the interval between the half-hour chime and the next set of hourly chimes

Adding these up yo get a total of 90 chime intervals in a 12 hour period with total interval length of 43200 seconds, for an average of 480 seconds or 8 minutes

Thus the average number of minutes between chimes is 8

Posted by Daniel on 2011-05-12 13:22:36