Question

A penny-farthing is a bicycle with a very large front wheel and a much smaller back wheel. Penny-farthings were popular in the 1800s and were available in different sizes. Suppose the diameter of one particular penny-farthing's front wheel is 48 inches and the ratio of the diameter of the front wheel to the diameter of the back wheel is 3:1. What is the circumference of the back wheel? Use 3.14 for 1.

Answer 1

Lets draw a picture of the penny-farthing bicycle:

where x is the diameter of the back wheel. Since the ratio is 3 to 1, we have

`(x)/(48)=(1)/(3)`

By moving 48 to the right hand side, we have

`\begin{gathered} x=(1)/(3)*48 \\ x=(48)/(3) \\ x=16 \end{gathered}`

This means that the diameter of the back wheel is 16 inches. Now, the circunference formula is

`C=\pi\cdot d`

where d is the diameter. Then, the circunference of the back wheel is

`\begin{gathered} C=3.14*16 \\ C=50.24\text{ in} \end{gathered}`

What is the circumference of the back wheel? 50.24 inches