Question

The length of the minute hand is 200% of the length of the hour hand.

In 1 hour, how much farther does the tip of the minute hand move than the tip of the hour hand? Round your answer to the nearest hundredth

Answer 1

Step-by-step explanation:

since lengh of minute hand is 200% of

hour hand

therefore

ratios of length between.

hour hand and minute hand= 1 : 2

lengh of hh= 20mm

length of mh= 40 mm

distance covered by hour hand in 1 hour

(since time taken to complete one round by hour

hand is 12 hours.)

= 2×pi× length/ time taken for complete 1 round

= 2× 20×pi/12=10pi/ 3 ( say it is X)

X=. 10pi/3....................(1)

similarly if length of minute hand be 2 unit then

distance covered by it in 1 hour

(since time taken to complete one round by

minute hand= 1 hour)

= 2×pi×40/ 1

= 80pi unit ( say it is Y)

Y = 80pi ......................(2)

Therefore difference of distances covered

by these two hands

= ( 80pi -10 pi/3)

=. (22/7)(80-10/3)

= 22×230/21

= 240.95 mm

since minute hand is 20 minute before

than the hour hand according as the

figure given.

=> difference between these two hands.

= 1- 20/60 of 240.95

2/3 of 240.95

= 160.63 mm

hence tip of minute hand will be 160.63

mm ahead from hour hand after one hour.