Then the distance it travels in a full rotation is 100 * pi cm.

So if we want to solve for RPM, let’s use “x” to designate that unknown.

In this case, 100 * pi centimeters * x / minutes = 400 miles / hours.

There are 60 minutes in an hour and approximately 160934 centimeters in a mile (according to Google.) So let’s get everything in the same units:

100 * pi centimeters * x / minutes = 400 * 160934 centimeters / 60 minutes

Now our centimeters and minutes can cancel out. We have

100 * pi * x = 400 * 160934 / 60

To solve for x, we can divide both sides by 100 * pi:

x = (400 * 160934) / (60 * 100 * pi)

which is about equal to 3417 revolutions per minute. (But you can use a calculator or something for more precise value.)