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 Overcomplicated? by Lisa)

But you did that in the real world, where tape recorder/players are made so that a certain constant number of inches per second (1 3/4) goes past the read-write heads.  In these real-world recorders, as more tape builds up on the take-up spool, so that spool starts to move more slowly (even in absolute speed the hub at a given distance from the center moves at a slower number of cm/sec).

Stan's cassette recorder/player works differently, as specified in the second bulleted item.  The take-up spool moves at a constant speed, so the tape is moving past the heads more slowly at the beginning of a side and faster at the end of a side.

Posted by Charlie on 2004-04-29 13:04:21