Diameter of wheel 

If a wheel travels 1 mile in 1 minute at a rate of 600 revolutions per minute. What is the diameter of the wheel in feet ? The answer to this question is 2.8 feet.


Could someone please explain how to solve this problem ?
 A: We are told that every minute, the wheel made $600$ revolutions. When a wheel makes one revolution, it travels forward by one circumference-length - here is an illustrative animation from Wikipedia (in this animation, the circle has radius 1):

Thus, in one minute, the wheel travels $600C$, where $C$ is the circumference of the wheel. Recall that $C=2\pi R=\pi D$ where $R$ and $D$ are the radius and diameter, respectively. 
Therefore, we want to solve
$$600\cdot \pi D\approx 1885D =5280\text{ft}.$$
A: If the diameter is $d$ miles, then we should have that $600 \pi d = 1$, because for each revolution the wheel would travel $\pi d$, which is the circumference of the wheel, and in one minute it spins $600$ times, thus travelling $600\pi d$ miles. Solving for $d$, we get $\displaystyle d = \frac{1}{600 \pi} = 0.00053051\ldots$. Since $d$ was expressed in miles, we convert to feet, multiplying by $5280$, and we obtain that the diameter is approximately $5280 \times 0.00053051 = 2.8010928$ feet.
Alternatively, we could have considered $d$ expressed in feet, and solved $600 \pi d = 5280$, that is, first converting the $1$ mile into $5280$ feet, and we would have obtained the same answer.
A: The distance travelled by a wheel in one revolution is nothing but the circumference. If the circumference of the circle is $d$, then the distance travelled by the wheel on one revolution is $\pi d$.
It does $600$ revolutions per minute i.e. it travels a distance of $600 \times \pi d$ in one minute. We are also given that it travels $1$ mile in a minute.
Hence, we have that $$600 \times \pi d = 1 \text{ mile} = 5280 \text{ feet}\implies d = \dfrac{5280}{600 \pi} \text{ feet} \approx 2.801127 \text{ feet}$$
