Question

The length of the minute hand is 150% 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 to the nearest hundredth.
The length of the minute hand is 150% of the length of the hour hand.

Answer 1

Answer:

17(pi)r/6

Step-by-step explanation:

Since neither hand length is known, you can have an answer in terms of one of the hands, but you cannot get just a number.

Let r = the length of the hour hand.

Then, the length of the minute hand is 150% of r = 1.5r.

The minute hand is the radius of the circle drawn by the tip of the minute hand. In 1 hour, the minute hand rotates one full revolution, so the tip of the minute hand moves the circumference of the circle drawn by the tip of the minute hand.

Now we find the circumference of the circle of the tip of the minute hand.

C = 2 * pi * r,

but the radius here is 1.5r, so we get

C_minute_hand =  2 * pi * (1.5)r

C_minute_hand = 3(pi)r

The hour hand rotates a full revolution in 12 hours, so it rotates 1/12 of a revolution in 1 hour. The radius is r.

C_hour_hand = 2 * pi * r * 1/12

C_hour_hand = (pi)r/6

The difference in how much each tip travels is

3(pi)r - (pi)r/6 = (pi)r(3 - 1/6) = 17(pi)r/6