Question

The odometer of a car reads 2000km at the start of a trip and 2400km at the end of the trip. If the trip took 8h, calculate the average speed of the car in \[km\,{h^{ - 1}}\]

Answer 1

Hint: We can find the total distance covered by subtracting the initial odometer meter from final odometer reading. Then we are also given the time taken to cover this distance. We can divide the total distance covered by total time taken to find the required average speed.

Complete step-by-step answer:
We are given the odometer reading of the car at the start of the trip is 2000km.
 $ \Rightarrow {d_{initial}} = 2000$
It is also given that the odometer reading at the end of the trip is 2400km.
 $ \Rightarrow {d_{final}} = 2400$
We know that the total distance covered by the car is by subtracting the initial odometer meter from final odometer reading. So, we can write,
 $ \Rightarrow {d_{total}} = {d_{final}} - {d_{initial}}$
On substituting the values, we get,
 $ \Rightarrow {d_{total}} = 2400 - 2000$
On simplification we get,
 $ \Rightarrow {d_{total}} = 400km$
Thus, the total distance covered is 400km.
It is given that the trip took 8 hours.
 $ \Rightarrow {t_{total}} = 8$
We know that the average speed of a moving body is given by the total distance covered divided by the total time taken.
 \[ \Rightarrow avg.\,speed = \dfrac{{{d_{total}}}}{{{t_{total}}}}\]
On substituting the values, we get,
 \[ \Rightarrow avg.\,speed = \dfrac{{400km}}{{8h}}\]
On simplification, we get,
 \[ \Rightarrow avg.\,speed = 50km\,{h^{ - 1}}\]
Therefore, the average speed of the car is \[50km\,{h^{ - 1}}\].
Thus, the required solution is \[50km\,{h^{ - 1}}\]

Note: Alternative method to find the average speed is given by the equation is given by,
We know that average speed is also given by the equation,
 \[ \Rightarrow avg.\,speed = \dfrac{{{d_2} - {d_1}}}{{{t_2} - {t_1}}}\]
Here we have, ${d_1} = 2000km$, \[{d_2} = 2400km\] ${t_2} = 8$ and ${t_1} = 0$. On substituting these in the equation, we get,
 \[ \Rightarrow avg.\,speed = \dfrac{{2400 - 2000}}{{8 - 0}}\]
On simplification, we get,
 \[ \Rightarrow avg.\,speed = \dfrac{{400}}{8}\]
On division we get,
 \[ \Rightarrow avg.\,speed = 50km\,{h^{ - 1}}\]
Therefore, the average speed of the car is \[50km\,{h^{ - 1}}\].