The wheels of a car have radius 13 in. and are rotating at 800 rpm. Find the speed of the car in mi/h.

Question

I have tried entering in 62, 61.8, and 61.9 as answers but all were wrong.

Answer 1

We know that the radius of the wheel is R = 13 in and frequency of revolution is 800 rpm. The problem asked us to find the speed in mi / hrs.

So, I will convert inches to miles and frequency to 1/ hrs. We will get R = 13 / 63360 mi.

And f = 800 x 60 = 48 000 1/hrs.

Using the formula for v = ωR and for ω = 2πf, we will have that linear speed

v = 2πfR

or

v = 2·3.14·13/63 360 mi · 48 000 1/ hrs = 61.848 mi / hrs.

Because all data in the problem were rounded to the whole number, the answer is 62 mi / hrs.

If you want, you can write it as 62 mph.

Answer 2

Ok, with a 13 inch radius, the circumference of the wheel is pi*13^2 (which is about 531 inches but we don't even need to bother plugging into the calculator yet, we can leave that 'til the end.

Here's the core relationships we'll want to tie together:

pi*13^2 inches

--------------

1 rotation

800 rotations

-----------------

1 min

60 min

---------

1 hour

1 mile

---------

63360 inches

... notice on each step, I take the units that were in a previous step and place them on the opposite side of the fraction of where they were before: taking something like

800 rotations 60 mins

------------------ * ---------------------

1 min 1 hour

will let minutes cancel out with minutes and give us 800*60 = 48000 rotations/hour (but, again, don't need to actually work that value out - can leave it as 800*60 'til the last step)

So we stack it all up like that:

pi*13^2*800*60/63360 ≈ 402.219 miles/hour (see how we don't need to actually touch a calculator 'til the end? This lets us go faster without losing track of what we were doing when we switch back and forth between paper and machine, and also will allow for a more accurate answer as we're not rounding along the way)

Check your learning management system's instructions for whether they're looking for a whole number, a specific number of digits, a specific number of decimals... from there. Note that if you're rounding this to the nearest tenth, it's 402.2 because the 1 means you'll round down, vs. if you're rounding to the nearest hundredth, it's 402.22 because the 9 means you'll round up.

I hope this helped!