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

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#### Jameson

Staff member
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

Staff member
Congratulations to the following members for their correct solutions:

1) Sudharaka
2) Reckoner

Solution (from Sudharaka):

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,

$d=100\pi x=r\pi y$

$\therefore r=\frac{100 x}{y}$

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