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= **Integrated Math 3--Period 4 Bike Wiki** =

**Distance Traveled vs. Gear Ratio**
**Having lots of gears on a bike makes bike riding more fun! You could be happily pedaling along, when you come upon a hill. This could really take the fun out of your ride. But if you have multiple gears you could switch to an easier gear and take the hill without having to expend much more energy than before. Good riders try to maintain a cadence of 80 to 100 pedal revolutions per minute. They manage to do this over varying conditions by shifting to a gear that will allow them to maintain that cadence. How far you travel per pedal stroke will differ according to the gear you choose, but the energy required to pedal should stay relatively constant.**

**Words you should know:**

**chainring** **front derailleur** **cogs** **rear derailleur** **shift levers**

**Below you will find functions that can be used to determine how far you will travel as a function of the number of turns of the pedals for five different gears on a 24-speed hybrid bike.**

Lowest Gear: Handle shifts both in position 1 (1-1) Mikey, Chris L., Jarrad, Chris A
Gear 1-1 has 28 teeth in the front and 32 teeth in the back the ratio is 0.875 f(t)=0.875t For ever one turn of the pedal, the rear gear turns 0.875. you multiply that by the # of turns you turn the pedal (t) and multiply by 26in. f(t)= 0.875(6.8ft) f(t)=5.95t

46 inch gear: Handle shifts in position 1-5 Ali, Marques, Val, Kieran, Aaron
The Diagrams show the position of the chain in the highest and lowest gears of multispeed bicycle. a.) You will be assigned a gear by your teacher. When the bicycle is in this gear, how many teeth are in the front gear? 28 and 17  b.) The ratio teeth in front gear is the number of turns the rear wheel makes for one full turn of the pedals. Find this ratio for the gear that you were assigned. 28/17=1.64 c.) Write an equation for the number of turns of the back tire as a function of the number if the turns of the pedals for the gear you were assigned. X= Number of times you pedals Y=Number of times the tire turns x(1.64)=y d.) Describe how you could use the function you wrote for part c) to find the distance traveled as a function of the number of turns of the pedals. (hint: The circumference of the rear tire is the distance your bicycle travels for one full turn of the rear wheel.) 3.14x26=81.64 x=number of pedals Y=how for the bike would move. X(1.64)(81.64)=133.88 134.32x=y

62 inch gear: Handle shifts in position 2-5 Angelo, John, Kayla, Andrew
-The front wheel has 36 teeth and the rear wheel has 16

-the ratio of the front gear and rear gear would be 38/16 or 2.375.

-An equation for the number of turns of the back tire and the number of the turns of the pedals is P(T)=2.375T.

-Using the function to find the distance traveled as a function the number of turns of the pedals would be:

-3.14x26=26x3.14= 81.68 inches (the circumference of tire)

-1 turn=2.375x81.68= 193.99 inches

78 inch gear: Handle shifts in position 3-5 Michel F, Mike C, Justin, Melvin
Gear 3-5 has 48 teeth in the front and 17 teeth in the rear the ratio is 2.82 d(x)=2.82x d(x)=73.32x

Hardest gear: Handle shifts in position 3-8 Jackie, Tasia, Chris C, Monica

 * Gear 3-8 has 48 teeth in the front and 11 teeth in the back
 * the ratio is 4.36
 * f(t) = 4.36(t) means that for every pedal the rear wheel will turn 4.36(t)
 * f(t)=29.70(t) means that for every one pedal the bike will go 29.70ft.