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A car travels a certain distance at the speed of 50km/h and returns with a speed of 40km/h. calculate the average speed of the whole journey.

Last updated date: 20th Jun 2024
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Hint: In this question we have been given only the speed of the car. We don’t have any information about the distance and the time taken. So, we have to assume the distance to be x and apply the basic formula for speed = distance/time ($S = \dfrac{D}{T}$); The question is asking about average speed, so the average speed will be equal to the total distance covered upon the total time taken which is given as
${S_{av}} = \dfrac{{{D_{total}}}}{{{T_{total}}}}$;

Complete step by step answer:
Step 1:
Calculate the total time taken and the total distance covered.
 The total distance is
X = x+x; (we have taken the distance of a car going and then returning)
The total time taken is
\[T = \dfrac{D}{S}\];
$\implies$ $T = {T_1} + {T_2}$ ;
$\implies$ ${T_1} = \dfrac{x}{{50}}$;
$\implies$ ${T_2} = \dfrac{x}{{40}}$;
Put the value,
$\implies$ \[T = \dfrac{x}{{50}} + \dfrac{x}{{40}}\]
$\implies$ \[T = \dfrac{{40x + 50x}}{{2000}}\]
$\implies$ \[T = \dfrac{{9x}}{{200}}\]
Step2: Calculate the average speed.
${S_{av}} = \dfrac{{{D_{total}}}}{{{T_{total}}}}$
Put values of total distance (2x) and total time (\[T = \dfrac{{40x + 50x}}{{2000}}\])
$\implies$ ${S_{av}} = \dfrac{{x + x}}{{9x/200}}$
$\implies$ ${S_{av}} = \dfrac{{2x \times 200}}{{9x}}$
The ‘x’ will cancel out
$\implies$ ${S_{av}} = \dfrac{{2 \times 200}}{9}$
Solve by dividing,
$\therefore $ ${S_{av}} = 44.44m/s$
Final Answer: The average velocity of the car is$44.44m/s$.

Note: There is another easy method of doing this question that will give you an approximate answer.
So average speed would be:
${S_{av}} = \dfrac{{2({S_1}{S_2})}}{{({S_1} + {S_2})}}$;
Here ${S_1} = 50km/h$ and ${S_2} = 40km/h$
Put the value and solve,
$\implies$ ${S_{av}} = \dfrac{{2(50 \times 40)}}{{50 + 40}}$;
Do mathematical calculation,
$\implies$ ${S_{av}} = \dfrac{{4000}}{{90}}$;
Solve further,
${S_{av}} = 44.44km/h$;