Question

How can we write the relation between miles and kilometers in the form of an equation?

Answer 1

Hint: In this question, we need to write the relation between miles and kilometers in the form of an equation. First, let us know the concepts and definition of miles and kilometres. Then by using direct variation, we can form the mathematical expression. We know that \[1\] mile is equal to \[1.6\] kilometres. Using this we can form the relation between miles and kilometers in the form of an equation.

Complete step-by-step solution:
Here we need to write the relation between miles and kilometers in the form of an equation .
First, let us know about miles and kilometers.
Miles(mi) is nothing but a unit which is used in the imperial and US customary for measuring length whereas kilometre (km) is nothing but the unit which is used for measuring the length in the international system of units.
Now we can form the relation between miles and kilometers in the form of an equation.
If \[x\] is directly proportional to \[y\] , which can be written as
\[\ y \propto x\]
According to the definition of proportionality,
We get,
\[\Rightarrow \ y = kx\] ••• (1)
Where \[k\] is the constant of proportionality.
We know that \[1\ \text{kilometre} = 0.621371\ \text{miles}\] or \[1\ \text{miles}\ = \ 1.60934\ \text{km}\]
Let us consider \[x\] miles and \[y\] kilometres and also the constant of proportionality is \[1.60934\]
Hence the equation (1) becomes,
\[y\ \text{miles}\ = 1.60934 \times x\ \text{kilometres}\]
Thus the relation is \[y = 1.60934x\]
We can also rewrite it in the reverse way also, that is \[x = 1.60934y\]
Let us consider an example to check the miles to km conversion formula.
We can convert \[5\] miles to kilometres using the miles to km formula.
By using miles to km conversion formula,
\[\Rightarrow \ y = 1.60934x\]
On substituting the values,
We get,
\[y = 1.60934 \times 5\]
On multiplying,
We get,
\[y = 8.04672\ km\]
Thus the \[5\] miles is equal to \[8.04672\ km\].

The relation between miles and kilometre in the form of an equation is \[y = 1.60934x\]

Note: The concept used in this problem is the direct variation. Direct Variation is nothing but the relationship between two variables in which one is a constant multiple of the other. If \[a\] is directly proportional to \[b\] , then the equation is of the form \[a = \ kb\] , where \[k\] is a constant of proportionality . We need to know that miles and kilometres are both units used to measure distance or length. Miles can be abbreviated as mi or m whereas Kilometres can be abbreviated as km. The equation \[y = 1.60934x\] is a very reliable method and the answers we get through equations are very accurate. We can also cross-check your answers using equations. The miles to km formula is used to calculate how much distance is travelled.