Stormy:
What is the origin of the word dragoon?
Answer: Dragoon originated in France, referring to soldiers whose rifle looked like breathed smoke and fire like a dragon.
I assume you have met Francis! :wink:
Let us linger for a moment to savour Mark's answer
STAGECOACH
If T is the time it took them to meet, then 16/T = T/9.
Therefore, T=12.
They took 21 and 28 hours to complete the journey.
(Followed by:)
I did it geometrically (d on the y-axis, t on the x-axis; you have lines that cross and there are similar triangles). However, since you asked, I decided to do it algebraically.
Call the stagecoaches X and Y, and say they meet at time T.
X took T hours to do what Y will do in 9 (X/Y = T/9)
Y took T hours to do what X will do in 16 (X/Y = 16/T)
T/9 = 16/T
Sweet, real sweet.
Let's check it out:
T= time to meet
Rf = rate of fast one
Rs = rate of slow one
D1 = short distance
D2 = long distance
D1 = Rf * 9 = Rs * T
D2 = Rs * 16 = Rf * T
T = Rf * 9 / Rs = Rs * 16 / Rf
Rf * Rf * 9 = Rs * Rs * 16
Rf * 3 = Rs * 4
Rs = 3 / 4 * Rf
D1 = Rf * 9 = Rs * T
T = Rf * 9 / Rs
T = Rf * 9 / (3 / 4 * Rf)
T = 4 / 3 * 9 = 12
Fast one = 9 + 12 = 21 hours
Slow one = 16 + 12 = 28 hours
Let us also not forget TTH also backed the winner!
There was an 18th century mathematician who lived on his parents' Patapsco River farm in Baltimore County, he was the first person ever to build a wooden clock in the United States. By taking apart a pocket watch, he figured out that the ratio of the gears was the key to making it all work. The clock struck every hour for more than forty years, keeping perfect time.
Suppose you have three gears:
A has 3 teeth.
B has 6 teeth.
C has 12 teeth.
They are all meshed. A B C
If Gear C moves clockwise three revolutions...
Will Gear B move clockwise or counter-clockwise
How many revolutions will it make
Will Gear A move clockwise or counter-clockwise
How many revolutions will it make