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. Note the hour hand is 20mm.
I am assuming that you want the distance of the hour and minute hands at 1 o'clock because there are different distances at a different time. Also, when the time goes from 6:00 to 7:00, the distance actually decreases.
If the hour hand is 20mm, then the minute hand is 40mm. At 1:00, the angle formed from the hour and minute hands is 30 degrees. I think the triangle formed might be an isosceles triangle, but I am not 100% sure. If it is an isosceles triangle, then the degrees are 30, 30, and 120.
For future reference to the triangle, the tip of the minute hand is point M, the tip of the hour hand is point H, and the center of the clock is point O.
Please tell me if my assumptions about the problem are correct or incorrect. I do not want to go too far if my explanation might not be suitable for this problem.
The 200% part is unclear....it the minute hand was 100% of the hour hand length, then they would be the same length.....so...200% indicates that the minute hand is twice as long as the hour hand....
If so....then the minute hand = 40mm
In one hour, the hour hand moves 30°
So....the distance the tip travels is (30/360)*2pi *20 ≈ 10.471 mm
In one hour, the minute hand travels 360°
The distance its tip travels is 2pi (40) ≈ 251.327 mm
So.....the minute hands travels ≈ [ 251.327 - 10.471] ≈ 240.86 mm farther