Question

. How many degrees, minutes, and seconds are respectively passed
over in 11+1/9 minutes by the hour and minute hands of a watch?

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Answer 1

Answer:

To compute the degrees of movement for the minute we need to start by figuring out what fraction of a right angle was passed over (11

9

1

minutes is less than 15 minutes or one quarter of an hour.) 11

9

1

=11.1111 (about.)

11.1111×60=666.66667 seconds

15×60=900 seconds

900

666.66667

=0.740741 (fraction of right angle passed over.)

90×0.740741=66.6667

60×0.6667=40

Therefore, movement of minute hand is 66 degrees and 40 minutes.

The hour hand is similar, except that over a period of an hour the hour hand will only move 1/12th of the clock face. This corresponds to 30 degrees. Therefore we need to compute what fraction of 60 minutes is 11.1111 minutes and apply that fraction to 30 degrees.

60

11.1111

=0.185185 (fraction of hour passed over.)

30×0.185185=5.5556 degrees

60×0.5556=33.336 minutes

60times0.336=20 seconds

Therefore, movement of hour hand is 5 degrees, 33 minutes and 20 seconds.