Problem of the week #29 - October 8th, 2012

[Jameson]

A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?
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[Jameson]

Congratulations to the following members for their correct solutions:

1) Sudharaka
2) Reckoner

Solution (from Sudharaka):

Spoiler

The circumference of the first wheel = \(2\pi\left(\frac{x}{2}\right)=\pi x\)

The wheel travels a distance equal to it's circumference in one revolution. Since \(d\) feet is covered in \(100\) revolutions,

\[d=100\pi x\]

Let \(r\) be the number of revolutions that the second wheel make when covering \(d\) feet. Then,

\[d=100\pi x=r\pi y\]

\[\therefore r=\frac{100 x}{y}\]