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.

So we know that the face of a clock is a circle, and that the hands of a clock start at the center and rotate around, well, clockwise.

Since the hands start at the center, we can think of each hand like the radius of a circle on the face of the clock.

The minute hand is longer, so when this makes a full rotation, the circle it makes will be bigger than the hour hand. Over the course of one hour, the distance will be much bigger.

How much bigger?

Well, we are measuring around the edge of a circle. That measurement is called the circumference, which is defined as π times the diameter, or π times twice the radius.

We have the radius of each circle relative to each other, such that the radius of the circle made by the minute hand is 200% longer than that made by the hour hand. So if r is the radius for the circle made by the hour hand, then that made by the minute hand is 3r. The circumference would also be three times larger.

We might be inclined to give that as our final answer, but remember that in one hour, the hour hand completes one full revolution, while the minute hand completes 60! So for one hour, the length traveled by the minute hand is actually 180 times that of the hour hand!

EDIT: I gave these values relative to each other because you would need to give the length of one of the hands to actually solve it.