Question

The tires of a racing bike are 28 inches in diameter. How far does the bike travel if the tires make 100 revolutions?

Answer 1

Remember that part of the bike tire is always touching the road. If the wheel has a diameter of 28 inches, and a radius of half that (14 inches), and if the wheel makes one full turn, how far forward does the bike go?

Please note: The circumference of a circle, C, has two formulas: C=Pi*d (where d is the diameter of the circle) and C=2Pi*r (where r is the radius of the circle). Take your pick. Find the circumference, C. What is the importance of this circumference in the math problem that you've posted?

Answer 2

Or: Imagine that you have plenty of leftover tape. You apply just enough tape to the tire to go all the way around the wheel on the very outside. How long will this piece of tape be? Hint: exactly the same length as the distance the bike will travel forward if the wheel makes one full turn.

Answer 3

So when I get the circumference, what's the next step?

Answer 4

How many times does the wheel turn, in this problem?

Once you know that (number of turns), what do you do towards finding the total distance that the bike moves forward?

Answer 5

Multiply by 100?

Answer 6

Yes. What units of measurement will your final answer have?

Answer 7

Feet and inches.
I got 8796 ft and 5 inches

Answer 8

Good start, Kailey, but 8796 feet comes to about 1 3/4 miles. Does that sound right for 100 turns of the wheel?

Answer 9

I don't know.

Answer 10

Let's please take your result and see what we can do with it. If you calculate the circumference by using the formula C=Pi*d, then the circ. is C = Pi(28 inches) = 8796 inches (not feet).

How many inches in one foot, Kailey?

Answer 11

12

Answer 12

Take a look at a foot-long ruler. It's divided into 12 inches. So: 12 inches = 1 foot.

We take 8796 inches and convert that into feet:\[\frac{ 8796~inches }{ 1 }*\frac{ 1~foot }{ 12~inches }\]Please (1) cancel out "inches," and (2), please divide 8796 by 12 to get the total number of feet the bike travels forward.

Answer 13

733?

Answer 14

Yes, 733 feet.

One more thing: Even though you're not asked to do so, you could convert 733 feet into miles:

\[\frac{ 733~feet }{ 1 }*\frac{ 1~mile }{ 5280~feet }\]

Answer 15

Would you please do this problem? Cancel out feet and divide 733 miles b y 5280.

Answer 16

Well the next question I was having trouble with involved miles. Using the same tire, how many revolutions will the tire make in a 50 mile race.

Answer 17

Let me ask you to review: What is the circumference of the wheel in feet?

Answer 18

733 feet. Right?

Answer 19

Hint:\[\frac{ 28~inches*\pi }{ 1 }\frac{ 1~foot }{ 12~inches }=?\]

Answer 20

733 feet represents the distance traveled by the bike if the wheel turns 100 times.
\[\frac{ 28~inches*\pi }{ 1 }\frac{ 1~foot }{ 12~inches }\]represents the circumference of the wheel in feet. It could not be 733 feet, could it?

Answer 21

No

Answer 22

the circumference of the wheel, in feet, is approx..... ???

Answer 23

I'm confused.

Answer 24

Simply evaluate the formula I gave you earlier:\[\frac{ 28~inches*\pi }{ 1 }\frac{ 1~foot }{ 12~inches }\]

Answer 25

this whole problem is mostly about conversion from one unit of measurement to another, so it's worth practicing such conversion.

Answer 26

Kailey: cancel out "inches." Divide 28 by 12. What do you get?

Answer 27

2.3

Answer 28

Good. Every time the wheel turns, the bike moves forward 2.3 feet. That does sound reasonable, doesn't it?

Now we're interested in knowing how many times the wheel turns in a 50-mile race. Is this your understanding too?

Answer 29

Yeah

Answer 30

OK. The race is 50 miles long. How many feet is that? All the info you need to calculate that is in our conversation, above. Please think about it.

Answer 31

Hint: 5280 feet = 1 mile

so

50 miles = ?? feet

Answer 32

264,000 feet.

Answer 33

Great. Divide that by 2.3 feet (the number of feet in one turn of the bike wheel). What do you get? What are the proper units of measurement?

Answer 34

114,782.6 feet

Answer 35

Not feet sorry.

Answer 36

Yes. Round that off a bit...say, to 114,800 TURNS OF THE WHEEL.

That's your answer. Please stop and think about this a bit. Does that answer seem reasonable or not, for a 50-mile bike ride, with each mile amounting to 5,280 feet?

Answer 37

Uh, yes?

Answer 38

I certainly think so. Please review our conversation once more. See if you have any questions, any comments, any doubts.

Answer 39

No questions. :) Thank you!

Answer 40

You're welcome. Hope to "see" you again on OpenStudy. Bye for now!