Question

An aeroplane covers 1020 km in an hour. How much distance will it cover in \[4\dfrac{1}{6}\] hours?

Answer 1

Hint: Here in the question we need to find the distance travelled by an aeroplane in \[4\dfrac{1}{6}\]hours. To find the distance travelled we can use the direct proportionality concept. When two quantities are varying in increasing (or decreasing) form then the ratio will remain constant, as the quantities vary directly it is defined as direct proportion.

Complete step by step solution:
We know that Speed can be calculated using distance and time as \[S = \dfrac{D}{T}\], from the question given as the distance increases time also increases. The ratio of distance and time are varying directly, then the ratio of their corresponding values also remains constant.
here \[\dfrac{{{D_1}}}{{{T_1}}} = \dfrac{{{D_2}}}{{{T_2}}}\] will be having same value that is Speed.
In the given question, the distance covered by an aeroplane in one hour is 1020 km.
Let \[{D_1}\]= 1020 km and \[{T_1}\] = 1 hour
Then speed can be represented as follows
\[ \Rightarrow \]\[S = \dfrac{{{D_1}}}{{{T_1}}}\]
\[ \Rightarrow S = \dfrac{{1020}}{1}\]
\[ \Rightarrow S = 1020\]Km --------- (1)
To find the distance \[{D_2}\] covered by an aeroplane in \[4\dfrac{1}{6}\] hours
Firstly, we will convert the hours given in mixed fraction to improper function
\[ \Rightarrow {T_2} = 4\dfrac{1}{6} = \dfrac{{25}}{6}\]
\[ \Rightarrow S = \dfrac{{{D_2}}}{{{T_2}}}\] --------- (2)
On substituting \[{T_2}\] value in equation (2)
\[ \Rightarrow S = \dfrac{{{D_2}}}{{\dfrac{{25}}{6}}}\] --------- (3)
On rearranging equation (3)
\[ \Rightarrow S \times \dfrac{{25}}{6} = {D_2}\] --------- (4)
On substituting the Speed value in equation (4)
\[ \Rightarrow 1020 \times \dfrac{{25}}{6} = {D_2}\]
On simplifying,
\[ \Rightarrow {D_2} = \dfrac{{25500}}{6}\]
\[ \Rightarrow {D_2} = 4250\]km
Therefore, the distance covered in \[4\dfrac{1}{6}\] hours will be 4250 km.
So, the correct answer is “4250 km”.

Note: Remember the unit of the distance and time should be the same, only then it can be represented in the ratio form and simplified further. The given question can also be solved in the unitary method. In the unitary method, we first find the value of one unit and then the value of the required number of units.