The radius of the front wheels of a cart is half that of the rear wheels. If the circumference of the front wheels is 1 meter and the cart traveled 1 kilometer, how many revolutions did the rear wheels make?

A. \(\frac{250}{\pi}\)
B. \(\frac{500}{\pi}\)
C. 250
D. 500
E. 750
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I thought we have to divided the distance i.e. 1000 meters with circumference i.e. 4\({\pi}\) and hence the answer should be \(\frac{250}{{\pi}}\)
but I guess in the solution you have divided the the distance with radius. Is it so?

are basically tryimg to find how many circumferences in the distance the cart travelled? So is resolution a full 360 degree circum?

thanks

What is the basic relation between Distance, Revolution, Circumference?

Is it Distance = No of Revolutions * Circumference ? Is this correct?

I guess it needs less math thinking than rational thinking. Hope I will explain well enough. Let's put the information we have together:

Radius of front wheel: r
Radius of rear wheel: 2r

This means that when the front wheel makes 1 whole revolution, the rear one makes 2. That because its diameter (2 radii) is twice as large, so it covers twice the distance of the front wheel at the same time (if the weels were not attached, when the front wheel covers 5 meters, the back would cover 10). Put differently, since the wheels are actually attached to the same vehicle, the distance the rear wheel has covered in the same amount of time with the front is half the distance of the front (if the front wheel covered 10 meters, the read wheel covered 5).

Now, we know that the circumference is 1 meter (so, in 1 meter the cart makes 1 revolution) and that the cart covered 1
km.

In others words:
1 revolution in 1 meter
x revolutions in 1000 meters?
x = 1000 for the front wheel, so x = 500 for the rear wheel.

Nice question, you don't even have to lift the pen to answer it.

I don't agree with the explanation. Question says radius is half- not circumference

I'm confused as to how the pie gets cancelled out. That confusion seems to be baked into the answer choices, hence me picking " 500/pie" rather than 500