Answer:
230.38 mm
Step-by-step explanation:
The distance traveled by the tip of the hands is (part of) the circumference of the circle with radius of the lengths of the hands.
[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]
Radii
Larger circle (minute hand):
- r = 200% of 20 mm = 40 mm
Smaller circle (hour hand):
Minute Hand
The minute hand does a full rotation of the circle in one hour.
Therefore, the distance it travels in one hour is the complete circumference of a circle with radius 40 mm:
[tex]\begin{aligned} \implies \textsf{Distance minute hand travels} & = \sf 2 \pi (40)\\ & = \sf 80 \pi \: mm\end{aligned}[/tex]
Hour Hand
There are 12 numbers on a clock.
The hour hand travels from one number to the next in one hour.
Therefore, the distance it travels in one hour is 1/12th of the circumference of the circle:
[tex]\begin{aligned}\implies \sf \textsf{Distance hour hand travels} & =\left(\dfrac{1}{12}\right)2 \pi r\\ & = \sf \left(\dfrac{1}{12}\right)2 \pi (40)\\& = \sf \dfrac{20}{3}\pi \: mm \end{aligned}[/tex]
To find how much farther the tip of the minute hand moves than the tip of the hour hand, subtract the latter from the former:
[tex]\begin{aligned}\implies \textsf{distance} & = \textsf{minute hand distance}-\textsf{hour hand distance}\\& = \sf 80 \pi - \dfrac{20}{3} \pi \\& = \sf \dfrac{220}{3} \pi \\& = \sf 230.38\: mm \:(nearest\:hundredth) \end{aligned}[/tex]
