Stan likes music, and likes oldies the best. In his collection of music he has a cassette tape of “The Cassettes 20 Greatest Hits”. The amazing thing about the 20 Greatest Hits, is that each hit is exactly 3 minutes long. This fits perfectly on a 60-minute tape.

Songs 1 – 10 are on Side A, while 11 – 20 are on Side B. When listening to the tape, Stan does one strange thing. He listens to the first 5 songs on side A, then flips it to the other side. He then listens to Side B from that point until the tape ends. How many songs does Stan hear?

• The tape is wrapped around two spools that have identical diameters of 1 cm.
• The spool that is receiving the tape rotates at a constant speed.
• The tape, when located all on one spool, measures 5 cm in diameter.

(In reply to solution by Charlie)

Charlie, it seemed to me you got messed up by the whole idea of tape speed past the read head, so I started solving this using cross-sectional area and geometry rather than tape length and calculus. Pretty soon, I saw that I had blundered in my gut instinct, and your solution was right (as usual)! Why did I ever doubt you?

Posted by Bryan on 2004-04-27 18:28:35