Need help with a Trig question

[mountainman]

Ok, Im kinda confused on a trig question I have for homework. Usually the answers are in the back to check the work, but not this one. Here is the question:

The diameters of the front and rear tires of a tractor are 36 in and 64 in respectively. Find the RPM of the front and rear tires when the tractor is traveling 9 miles/hour.

Now, here is my figuring:

9 miles 1 5280 12 1 rev 1 hour
---------- * ---- * -------- * ----- * ------- * ---------
1 hour 18in 1 mile 1 ft 2PI 60minutes

So that reads 9 MIles over 1 Hour * 1 over 18 inches * 12 inches over 1 foot * 1 Rev over 2PI * 1 hour over 60 minutes. The 1 Rev over 2PI tranfers the answer to angular velocity needed for the RPM measurement, the 1 hour over 60 minutes gets rid of the hour under the 9 Miles, the 5280 ft gets rid of the miles and transfers to feet, and then the 12 inces over 1 ft gets rid of the feet. NOW, the answers I got were
84 rpm for the small wheel 36 in diameter
47.2rpm for the large wheels 64in diameter.

Am I right or totally off base?

[pbharris]

hey mountainman,
figure the number inches per minute which gave me 9504 in/min.

From here I did a 2*pi*r * (x) RPM = 9504 in/min (because 2*pi*r = 1 rev /min)

then i did a

9504 in
---------------- = (x) RPM
2pi*r in min

solving for each x gave me:

64 inch wheel = 23.63 RPM
36 inch wheel = 42.01 RPM

Then I scratched my head wondering why, why 'o' why my answers were double yours - then i saw it, i had the 64 and 36 as radius - so - your answers are correct.

You totally right.