Question

On a map with a scale factor $1:10,000,$ the distance between two nearby cities is $4\text{inches}.$ Find the actual distance between the two cities in miles (correct upto $2$ decimal places).

• A. $1.26$
• B. $0.63$
• C. $63.00$
• D. None of the above.

Answer 1

The correct option is B $0.63$

$\text{Given:}$
$\bullet$ Distance on map $=4\text{inches}$
$\bullet$ Scale factor $=\frac{1}{10,000}$

We know that,
$\text{Scale factor}$
$=\frac{\text{Dimension of scale model}}{\text{Dimension of actual object}}$

$\Rightarrow$ $\frac{1}{10,000}=\frac{4}{\text{Actual distance}}$

Inverting the fractions,
$\Rightarrow$ $\frac{10,000}{1}=\frac{\text{Actual distance}}{4}$

Multiplying both sides by $4$,
$\Rightarrow \frac{10,000}{1}\times 4=\frac{\text{Actual distance}}{4}\times 4$
$\Rightarrow 40,000=\text{Actual distance}$

Thus, actual distance between the two towns = $40,000\text{inches}$

But, we need the distance in miles.

$1\text{mile}=5,280\text{feet}$
$1\text{foot}=12\text{inches}$

$\therefore 1\text{mile}=5,280\times 12\text{inches}$
$=63,360\text{inches}$

Actual distance between the two towns = $40,000$ inches
= $\frac{40,000}{63,360}\text{mile}$
$\approx 0.63\text{mile}$

Hence, option (b.) is correct.