Question

It's 3 o' clock on the Kentucky State Capitol Clock. The tip of the hour hand (h) is 25 ft from the tip of the minute hand (m). At 6 o' clock, the tips are 35 ft from each other. How far are the tips when it is 12 o' clock? (For 3 o' clock use $h^2+m^2={25}^2$)

• A. 25 ft
• B. 5 ft
• C. 16 ft
• D. 4 ft

Answer 1

The correct option is B 5 ft

We have to find the distance in the following configuration.
Let the length of the hour hand be ‘h’ and the length of the minute hand be ‘m’. We have to find $m-h$.
At 6 o'clock:
$h+m=35$
$h^2+m^2={25}^2=625$
$(h+m{)}^2={35}^2=1225$
$h^2+m^2+2hm=1225$
$2hm=1225-625=600$
$(m-h{)}^2=h^2+m^2-2hm=625-600=25$
$m-h=5ft$