Driving In Circles

Geometry Level 2

A horse carriage was going in a circle. When it completed the circle, an observer realized that the inner wheel made 5 complete revolutions, and the outer wheel made 8 complete revolutions.

If the distance between the wheels is 6 feet, what is the diameter of a wheel?

Note: The wheels have the same diameter

2 feet 5 feet 4 feet 3 feet

Chung Kevin by Chung Kevin , 45, Australia

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1 solution

Marta Reece
Apr 16, 2017

Inner wheel travels distance of 2 π r 2\pi r per trip around. Outer wheel travels 2 π ( r + 6 ) 2\pi(r+6) per trip.

If the radius of the wheel is R R , the problem can be written as a system of equations.

2 π r = 5 × 2 π R 2\pi r=5\times 2\pi R

2 π ( r + 6 ) = 8 × 2 π R 2\pi(r+6)=8\times 2\pi R

Which can be simplified to

8 R = r + 6 8R=r+6

5 R = r 5R=r

And have a solution R = 2 R=2 , or diameter of the wheel equal to 4 4 .

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