9. Kevin wrote the following explanation:
The minute hand of a clock makes I revolution in an hour, so it
moves through 360° every hour. The hour hand makes only
of a revolution in an hour, so it moves through 30° every hour.
If I let t represent the time (in hours) since 12:00, then 360t
represents the number of degrees through which the minute
hand moves and 30t represents the number of degrees through
which the hour hand moves. When the minute hand catches up
with the hour hand for the first time, it has completed I revolution
more than the hour hand, so I must subtract 1 from 360t before
setting it equal to 30t. So, 360t - 1 - 30t.
The hands of a clock
coincide at 12:00. At what
time, to the nearest second,
do the hands again coincide?
Explain the error in Kevin's reasoning. Then correct the error and finish solving
the problem.