Question 550625: Suppose the tip of the minute hand of a clock is two inches from the center of the clock. For each of the following durations, determine the distance traveled by the tip of the minute hand.
Question 1: 15 minutes and Question 2: 10 and a half hours.
Not sure at all how to approach this problem.
Found 2 solutions by Alan3354, bucky:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Suppose the tip of the minute hand of a clock is two inches from the center of the clock. For each of the following durations, determine the distance traveled by the tip of the minute hand.
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r = 2 inches
The minute hand's tip travels 1 rev/hr = 2*pi*r inches = 4pi inch/hr
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Question 1: 15 minutes
15 mins = 1/4 hr
d = (1/4)*4pi = pi inches
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and Question 2: 10 and a half hours.
d = 10.5*4pi = 42pi inches
Answer by bucky(2189)  (Show Source):
You can put this solution on YOUR website! The minute hand will make one complete rotation in an hour (60 minutes). Picture that at the start of an hour, the minute hand is pointed at the 12 on the clock. It then begins a slow rotation around the clock until 60 minutes later it arrives at the position where it again points to the 12. How far has the tip of the minute hand traveled during that hour? It has traveled the complete circumference of a circle that has a radius of 2 inches. So you can write an equation for this distance as:
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Where C stands for the circumference of the circle and r stands for the radius, and the equation is just the standard equation for finding the circumference of a circle if you know the radius.
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In this problem, the radius is 2 inches and therefore you can substitute 2 for r and you will find the circumference in inches. This is as follows:
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which by multiplying out the right side simplifies to:
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 inches
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You can convert this to a more common form by substituting 3.1416 as the value for  and multiplies out as follows:
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 and this becomes  inches per hour.
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So for each hour the tip of the minute hand travels  inches or an equivalent numerical value of 12.5664 inches.
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Now to answer the questions that you are asked in the problem. First, how far does the tip of the minute hand travel in 15 minutes? 15 minutes is a quarter (one-fourth) of an hour. So in 15 minutes the tip of the minute hand travels one-fourth of the distance it would travel in an hour. So, using D to represent the distance the tip moves we can say that for 15 minutes the tip moves:
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And dividing out the right side, you get that in 15 minutes the tip of the minute hand moves:
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inches which numerically is  inches
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Next, how far does the tip of the minute hand travel in 10 and a half hours? Since each hour it travels inches, in 10 hours it will travel a distance of:
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 which multiplies out to  inches.
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Then in the additional half hour the tip, since the tip moves inches in an hour, it will move half that distance in the half hour. In other words, in the half hour it moves half of inches, or it moves  inches. So in 10 and a half hours it moves the sum of these two distances which is:
.
 inches and this totals to  inches
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As before you can convert this to numerical inches by substituting 3.1416 for to get:
.
 inches and this multiplies out to  inches.
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Hope this helps you to understand how to work clock problems such as this one.
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