Chapter 4.1, Problem 61E

Solution

To identify: The correct option a bicycle with 26-in-diameter wheels is travelling at 10mph. To the nearest whole number, how many revolutions does each wheel make per minute

Option (B) is correct option. 129 revolution per minute are required by the bicycle

Given information:

The bicycle with 26-in-diameter wheels is travelling at 10mph. The options are:

Options (A) $54$

Options (B) $129$

Options (C) $259$

Options (D) $406$

Options (E) $646$

Explanation:

Consider the given information

Observe that radius of the bicycle wheel is $\frac{26}{2}=13inches$ .

Consider the number of revolutions per minutes to be $x$

Then convert revolution per minutes to miles per hour by a series of unit conversion factors

  $\frac{x\text{rev}}{\text{1}\text{min}}\times \frac{60\min }{\text{1}\text{hr}}\times \frac{2\pi }{\text{1}\text{rev}}\times \frac{13in.}{\text{1}\text{radian}}\times \frac{\text{1}\text{ft}}{\text{12}\text{in}\text{.}}\times \frac{1\min }{5280\text{f}t}=10\frac{\text{mi}}{\text{hr}}$

Simplify to obtain

  $\begin{array}{c}x=\frac{10\times 5280\times 12}{60\times 13\times 2\pi }\\ =\frac{5280\times 2}{13\times 6.28}\\ =129\end{array}$

Hence 129 revolution per minute are required by the bicycle

So the correct option is (B).