Chapter 7, Problem 12PT

To determine

To find:The scale factor of model to actual car.

Answer to Problem 12PT

The scale factor of model to actual car is $1:18$ .

Explanation of Solution

Given information: The given information is:

The actual length of car is $10\text{feet}$ and $6\text{inches}$ .

The model has a length of $7\text{inches}$ .

Calculation:

A scale factor is a unit less ratio.

Use the conversion factorto $\frac{\text{12}\text{in}\text{.}}{\text{1}\text{ft}}$ rewrite $\text{10}\text{ft}\text{6}\text{in}$ .

  $\begin{array}{l}\text{10}\text{ft}\text{6}\text{in=10}\text{ft×}\frac{\text{12}\text{in}}{\text{1}\text{ft}}\text{+6}\text{in}\\ \text{10}\text{ft}\text{6}\text{in=120}\text{in}\text{.}\text{+6}\text{in}\text{.}\\ \text{10}\text{ft}\text{6}\text{in=126}\text{in}\text{.}\end{array}$

The scale factor of model to actual car is:

  $\begin{array}{l}\text{Scale factor}\text{=}\frac{\text{Model}\text{length}}{\text{Actual}\text{length}}\text{=}\frac{\text{7}\text{in}\text{.}}{\text{10}\text{ft}\text{6}\text{in}\text{.}}\\ \text{Scale factor=}\frac{\text{Model}\text{length}}{\text{Actual}\text{length}}\text{=}\frac{\text{7}\text{in}\text{.}}{\text{126}\text{in}\text{.}}\\ \text{Scale factor=}\frac{\text{Model}\text{length}}{\text{Actual}\text{length}}\text{=}\frac{\text{1}}{\text{18}}\end{array}$

Therefore,thescale factor of model to actual car is $1:18$ .