Finding revolution of different sized wheels

[slambert56]

Ok the answer in the back of my book says 974 revolutions and a very short hand way to get that is divide the big wheel radius by the small wheel radius to get 3.53 so i can just multiply 3.53 times the 276 rev to get 974 rev. But I tried a long way using the s=rtheta formula b/c on a test I probably can't get all points without using a formula. I got a different answer and I don't know why. Any help would be greatly appreciated!

Here is the question and my work is in the picture.
A penny farthing bicycle(has a large front wheel and a small rear wheel). On a sunday ride teh front wheel(r=1.20m) makes 276 revolutions. How many revolutions does the rear wheel(r=.340m) make?
Okay so I simply use the formula s=r times theta. I know to use this formula I have to have radians and I converted and then at the end convert back to revolutions. i rev=2pie radians.

Now I first found the total distance traveled by the big wheel by finding s which is the distance and this is the same for the small wheel so i just plugged it in. Am I missing something?? THANKS.
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[nasu]

You should post this in the homework section.
How did you get that 6120 divided by 2π is 9614? What value of π are you using?

 

[slambert56]

I just divided 6120 by 2pie just to convert radians into revolutions. 1 rev= 2 pie radian

 

[nasu]

My question was about your numbers. How much is 6120 divided by 2π?

 

[slambert56]

ahhhhh okay when i typed it into my calculator as (2pie) and it didnt multiply apparently. Its 974. Thanks for catching my dumb mistake. I thought it would automatically multiply but I have to put in the sign.