Question

On a map with a scale factor $1:10000,$ the distance between two nearby cities is $4$ inches. Find the actual distance between the two cities in miles (upto $2$ decimal places).
(Note: $1$ foot $=12$ inches, $1$ mile $=5280$ feet)

• A. $0.63mi$
• B. $12.63mi$
• C. $1.63mi$
• D. $2.63mi$

Answer 1

The correct option is A $0.63mi$

Given:
$\bullet$ Distance between two cities on the map $=4in$
$\bullet$ Scale factor $=\frac{1}{10000}$
We know,
$\text{Scale factor}=\frac{\text{dimension of scaled model}}{\text{dimension of actual object}}$
$\Rightarrow \frac{1}{10000}=\frac{4}{\text{actual distance}}$
Multiplying both sides by $10000,$
$\Rightarrow 1=\frac{40000}{\text{actual distance}}$
$\Rightarrow \text{Actual distance = 40000 in}$

Thus, actual distance between the two cities $=40000$ in
$1mi=5280ft$
$1ft=12in$
Therefore, $1mi=5280\times 12in$
$=63360in$

Actual distance between the two cities $=40000in$
$=\frac{40000}{63360}mi$
$\approx 0.63mi$