Question

A car covers the first 2km of the total distance of 4km with a speed of 30km/h and the remaining distance of 2km with a speed of 20km/h. The average speed of the car is:
$
  {\text{A}}{\text{. 24km/h}} \\
  {\text{B}}{\text{. 25km/h}} \\
  {\text{C}}{\text{. 50km/h}} \\
  {\text{D}}{\text{. 26km/h}} \\
$

Answer 1

Hint: We are given the total distance covered by the car and two velocities. First we need to find out the time taken with each velocity and distance. Then average velocity can be found as the total distance upon total time taken for the whole journey of the car.

Formula used:
The average velocity is given by the following formula:
\[{V_{avg}} = \dfrac{d}{t}\]
where d represents the total distance covered while t represents the total time taken.

Detailed step by step answer:
We are given that a car covers a total distance of 4km in two parts.
$d = 4km$
First the car covers 2 km with a speed of 30 km/h for the first part of a journey of 4km. From these we can calculate the time taken for the first part of the journey.
$
  {d_1} = 2km \\
  {V_1} = 30km/h \\
  \therefore {t_1} = \dfrac{{{d_1}}}{{{V_1}}} = \dfrac{2}{{30}} = \dfrac{1}{{15}}h \\
$
We are given that for the rest of the journey the speed of the car is 20 km/h. Therefore the time taken for the second part of the journey is given as
$
  {d_2} = 2km \\
  {V_2} = 20km/h \\
  \therefore {t_2} = \dfrac{{{d_2}}}{{{V_2}}} = \dfrac{2}{{20}} = \dfrac{1}{{10}}h \\
$
So, the total time taken for the total distance of 4 km can be given as follows:
$t = {t_1} + {t_2}$
Now, substituting the calculated values of time, we get
$t = \dfrac{1}{{15}} + \dfrac{1}{{10}} = \dfrac{1}{6}h$
Now we can calculate the average velocity by dividing the total distance covered by the total time taken as shown below.
\[{V_{avg}} = \dfrac{d}{t} = 4 \times 6 = 24km/h\]
This is the required answer and the correct option is option A.

Note: The student might assume that taking the average of the two velocities will give the average velocity required here but the definition of average velocity states that it is equal to the ratio of total distance covered to the total time taken.