I have never seen a school bus like this. Source.

I’m going to try to ease myself back into posting math questions fairly regularly on here. No prizes for now, just the satisfaction of knowing you were the first person in the world besides me to figure this particular question out. This probably wouldn’t appear on the SAT, but it exercises the same muscles you’ll need to flex to do well.

The wheel diameter on a certain school bus is 40 inches. A sensor on one wheel indicates that over a 20 minute period, the wheel made 9250 revolutions. Assuming the wheel did not slip at all, what was the average speed of the bus, in miles per hour, for those 20 minutes? Round your answer to the nearest whole number. (12 inches = 1 foot; 5280 feet = 1 mile)

Have at it!

UPDATE: John got it. Well done, sir.

The first important thing that you need to remember about wheels is that when they roll one revolution, they travel one circumference—as long as they don’t slip. Here’s an awesome illustration of that for a wheel with a diameter of 1 (and therefore a circumference of π):

Pi-unrolled slow

So, since the wheels on our bus have a diameter of 40 inches, each revolution of one of our wheels moves the bus 40π inches.

The wheel makes 9250 revolutions in 20 minutes, so the bus travels 9250•40π ≈ 1,162,389 inches in 20 minutes.

Convert that to feet: 1,162,389 inches ÷ 12 inches/foot ≈ 96,866 feet

…then to miles: 96,866 feet ÷ 5,280 feet/mile ≈ 18.35 miles

The last step, of course, is remembering that you need to get miles per hour, and this bus has only been traveling for 20 minutes. Speed = distance ÷ time, so our bus’s speed in miles per hour is:

Of course, since you’re probably working on your calculator, you should try not to round at intermediate steps like I did. Here’s a super-precise answer from Wolfram Alpha.

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