## A Clock Puzzle (second answer)

The second puzzle: We sometimes are told that when we drive, we should place our hands on the steering wheel at ten minutes to two. But if the steering wheel were really a clock, then at 10 minutes to 2 the right hand (pretending that the two hands of the clock are the same length) would be slightly higher than the left hand. We might drive in circles, using that advice. A minute or so later, the hands will be at equal heights. What time would that be?

Answer: Here is an easy way to do it. Let's start at 2:00 and go backward in time. But let's pretend that the minute hand goes forward, not backward. Then the solution is when the two hands coincide. The two hands are 60 degrees apart. We can use a degree as a unit of length, and use the distance=speed x time (d=st) formula. The minute hand moves at a speed of six degrees per minute. The hour hand moves at a speed of 30 degrees per hour or 1/2 degree per minute. They will coincide when 6t + t/2=60. Solving for t, we get 120/13 minutes (9.230769... min.). So the answer is 9.230769... minutes to two.

Third puzzle: Besides at 12:00, are the hour, minute, and second hands ever superimposed (assuming that they do line up at 12:00)?