Problem: Henry starts a trip when the hands of the clock are together between 8 a.m. and 9 a.m. He arrives at his destination between . and . when the hands of the clock are exactly apart. The trip takes:
Answer Choices:
A. 6 hr .
B. 6 hr . 43-7/11 min.
C. .
D. 6 hr .30 min .
E. none of these
Solution:
Let be the number of degrees the hour hand moves in the time interval between . and the beginning of the trip, and let be the number of degrees it moves between 2 p.m. and the end of the trip. The number of degrees traversed by the minute hand during these intervals is and , respectively. Since the minute hand traverses 12 times as many degrees as the hour hand in any given interval, we have
that is, the hour hand is just as many degrees past the 8 at the beginning as it is past the 2 at the end of the trip. Since the 8 and the 2 are apart, the initial and final positions of the hour hand differ also by , so that (A) is the correct choice.