Question

How long is $\dfrac{7}{10}$ of a mile, in feet?

Answer 1

Hint: The easiest way to solve this problem is by converting $1mile$ into yards and then convert the yards into the corresponding feet by unitary method. At the end, we must convert the fraction of the mile, that is, $\dfrac{7}{10}mile$ into the corresponding feet.

Complete step-by-step solution:
There are various systems of measurements like SI system, FPS or the US system and so many more. As far as length measurement is concerned, SI system includes metre, kilometre, and others, and the FPS system includes foot, yards, miles and others.
In the SI system, the basic unit of length is metre. Every other unit of length is expressed as some form of metre. For example, kilometre means $1000$ metres, where “kilo” stands for “thousand”, centimetre means $0.01$ metre, where “centi” stands for “one hundred” and so on. Here, we can clearly know what form of metre is the unit if we are well aware of these terms. In the FPS system however, no such method is used. Here, every unit has a unique and specific name, like miles, yards, feet, inches, and so on. So, there are various conversion formulae for the FPS system which we must remember. We must know how many inches make a foot, how many feet make a yard and how many yards make a mile. Only then can we convert any unit into another.
Now, coming to the question, we start with the definition of a mile. The definition of a mile is
$1mile=1760yards$
The definition of a yard is
$1yard=3feet$
Therefore, we use the unitary method now.
If, $1yard=3feet$
Then, $\Rightarrow 1760yards=3\times 1760feet$
Which gives, $\Rightarrow 1760yards=5280feet$
Thus, $\Rightarrow 1mile=1760yards=5280feet$
By $\dfrac{7}{10}$ of a mile, we mean $\dfrac{7}{10}\times 1mile$ which is $\dfrac{7}{10}mile$ . Thus,
 $\Rightarrow \dfrac{7}{10}mile=\dfrac{7}{10}\times 1760yards=\dfrac{7}{10}\times 5280feet$ which gives,
$\Rightarrow \dfrac{7}{10}mile=1232yards=3696feet$
Therefore, we can conclude that $\dfrac{7}{10}mile=3696feet$.

Note: We must remember all the conversion formulae of the units; otherwise we cannot solve these types of problems. Whenever it is given in the question that “some fraction of a unit” we must multiply the fraction with the unit and then convert it into some other unit. At the end of the conversion, we must remember to convert the fraction form of the unit, otherwise our conversion will remain incomplete.