# Thread: Finding how many revolutions a car will make dirving a certain amount of miles?

1. ## Finding how many revolutions a car will make dirving a certain amount of miles?

Algebra II question, I've tried everything above and beyond unit conversions and I cannot figure this out. If someone would explain to me how to do this problem I would be very greatful. The lesson this homework is based off of is based on Direct / Inverse variations.

You are going to drive 480 miles today at an average speed of 60 miles per hour. Thus you are going to drive for a total of (8) hours. The diameter of the wheels on your car (including tires) is 25 inches. Thus each wheel is going to turn a total of _______ times today.

2. Originally Posted by Lvl80
Algebra II question, I've tried everything above and beyond unit conversions and I cannot figure this out. If someone would explain to me how to do this problem I would be very greatful. The lesson this homework is based off of is based on Direct / Inverse variations.

You are going to drive 480 miles today at an average speed of 60 miles per hour. Thus you are going to drive for a total of (8) hours. The diameter of the wheels on your car (including tires) is 25 inches. Thus each wheel is going to turn a total of _______ times today.

Circumference of a tyre : $C = \pi D$ (where D is diameter)

The distance covered in one resolution is equal to C

Thus $n_C = \dfrac{480}{C} \cdot k$ (where k is the conversion factor between inches and miles and k>1 )

3. Hi

Circumference = 2*pi*r
1 mile = 63360 inches

Can you continue from here?

4. Thanks both of you. For e^'s formula, I would plug in 78.5 for C (having done 25 * pi) then multiply it by 63360 / 1 mile to convert it into inches, right? Then the answer for Nc would be

Nc = 480 / 78.5 * 63360 / 1, which = 10362 revolutions. Is this correct?

5. Ah, I found my error in the above post. In the above post I attempted to cross multiply, which I do not have to do. After doing

Nc = 480 / 78.5 * 63360 / 1

I got 387424 as my answer, which is correct. Thanks to both of you for helping me with this. The whole concept is still a bit foggy, but I'm getting it.

6. 480 miles is 480*63360=30412800 inches.
1 revolution is 2*pi*r=2*3.142*12.5=78.5389 inches
Total revolutions is 30412800/78.5389=387228
So each wheel will travel 387,228 revolutions.

7. $n_C = \dfrac{480}{25\pi} \cdot 63360 = 387227$

I don't know if your book told you to round pi off to a certain value, if so use that value and disregard this one.

Normally, you'd not round off until the end of a sum