Question

How would I convert 140 km to miles if the only information I was given in the question is there are 5280 feet in a mile?

Answer 1

Hint: 140 km is to be converted to miles whereas it is given that there are 5280 feet in a mile. Here we have to use the relation between km and feet which is $1{\text{ km}} = 3280.84{\text{ ft}}$. Using this, first convert 140 km into feet and then convert it in miles using the relation given in the question.

Complete step-by-step solution:
According to the question, we have to convert 140 km into miles and it is given that there are 5280 feet in miles.
If we write the given information in equation, we have:
$ \Rightarrow 1{\text{ mile}} = 5280{\text{ ft }}.....{\text{(1)}}$
Now, to convert 140 km into miles we will have to use the relation between km and feet which we already know. This is shown below:
$ \Rightarrow 1{\text{ km}} = 3280.84{\text{ ft}}$
For 140 km, we’ll apply a unitary method.
If 1 km is equivalent to 3280.84 feet then 140 km will be equivalent to the product of 140 and 3280.84 feet.
$
   \Rightarrow 140{\text{ km}} = 140 \times 3280.84{\text{ ft}} \\
   \Rightarrow 140{\text{ km}} = 459317.6{\text{ ft}}
 $
Now we’ll use equation (1) and we have:
If 5280 feet is equivalent to 1 mile then 459317.6 feet will be equivalent to the division of 459317.9 by 5280 miles.
$
   \Rightarrow 140{\text{ km}} = \dfrac{{459317.6}}{{5280}}{\text{ miles}} \\
   \Rightarrow 140{\text{ km}} = 86.99{\text{ miles}} \approx 87{\text{ miles}}
 $

Thus 140 km is equivalent to 87 miles approximately.

Note: Using unitary methods, we solve the problem by first finding the value of one unit and then finding the required value by multiplying the single unit value with necessary value. This method is widely used in time and distance problems and in time and work problems.
Like in the above question, first we recalled how many feet there are in 1 km and then we determined if for 140 km using a unitary method. And then we utilized this along with the question’s information to find the answer.