Chapter 6.6, Problem 1CYU

To determine

To find: The scale of a shown model car, that’s actual length is $14\frac{1}{2}$ feet and its length in model is $7\frac{1}{4}\text{inches}$ .

Answer to Problem 1CYU

Required scale is $\frac{1}{24}$.

Explanation of Solution

Given information: 

A model of a car is given so that actual length of car is $14\frac{1}{2}$ feet and its length in model is $7\frac{1}{4}\text{inches}$ .

Concept used:

In similar objects, sizes are different, so the required scale is given as:

  $\text{Scale}=\frac{\text{Actual length of car}}{\text{Length of modal car}}$

Further also use the conversion formula that,

  $1\text{ foot}=12\text{inches}$

Calculation:

Based on above conversion formula, actual length of the car

  $14\frac{1}{2}\times 12=\frac{29}{2}\times 12=174\text{inches}$

So, required scale $=\frac{174}{7\frac{1}{4}}=\frac{174}{\frac{29}{4}}=\frac{174\times 4}{29}=6\times 4=24$

Based on above concept, the required scale is $\frac{1}{24}$ , that means the length of actual car is 24 times greater than the length of given model car.