SOLUTION: The 100-foot clock tower in Rome, Georgia is more than 100 feet tall. The minute hand is 4 feet, 3 inches long, and the hour hand is 3 feet, 6 inches long. How many inches farther

Algebra ->  Circles -> SOLUTION: The 100-foot clock tower in Rome, Georgia is more than 100 feet tall. The minute hand is 4 feet, 3 inches long, and the hour hand is 3 feet, 6 inches long. How many inches farther       Log On


   

Question 948668: The 100-foot clock tower in Rome, Georgia is more than 100 feet tall. The minute hand is 4 feet, 3 inches long, and the hour hand is 3 feet, 6 inches long. How many inches farther does the tip of the minute hand travel than the tip of the hour hand in one day?
I'm not quite sure how to do this, but I have a few things that I know: the minute hand HAS to travel more because it moves more than the hour hand. The circumference (if drawn) with radius of the minute hand will be 102pi inches and the the circumference (if drawn) for the hour hand will be 84pi inches. Not sure where to.go from there.
Found 2 solutions by macston, stanbon:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
The hour hand makes 2 revolutions per day (1 revolution/12 hours)
The minute hand makes one revolution per hour for 24 revolutions per day.
I'll use your numbers:
Hour %2884%28pi%29in%2Frev%29%282+rev%2Fday%29=168%28pi%29inches%2Fday
Minute %28102%28pi%29in%2Frev%29%2824+rev%2Fday%29=2448%28pi%29inches%2Fday
Difference 2448%28pi%29in-168%28pi%29in=2280%28pi%29in
ANSWER The minute hand travels 2280(pi)inches more than the hour hand (or 190(pi)feet)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The 100-foot clock tower in Rome, Georgia is more than 100 feet tall. The minute hand is 4 feet, 3 inches long, and the hour hand is 3 feet, 6 inches long. How many inches farther does the tip of the minute hand travel than the tip of the hour hand in one day?
I'm not quite sure how to do this, but I have a few things that I know: the minute hand HAS to travel more because it moves more than the hour hand. The circumference (if drawn) with radius of the minute hand will be 102pi inches and the the circumference (if drawn) for the hour hand will be 84pi inches. Not sure where to.go from there.
-----
One day is 24 times around for the minute hand and 2 times around for
the hour hand.
---
Circumference = pi*(2r)
-------------------------------
Minute hand distance:: 24*(pi)*(2*52")
----
Hour hand distance:: 2*pi(2*42)
-----
Ans: 2496pi - 168pi = 2328pi inches
----------------
Cheers,
Stan H.
------------------