A car travels from stop A to stop B with a speed of 30 km/h and then returns back to A with a speed of 50 km/h. Find average speed of the car.

For first part of the journey:

Distance travelled$=AB$

Speed of the car$=30\ km/h$

Time taken for the the journey$=\frac{distance}{speed}$

$=\frac{AB}{30}\ km$

For the second part of the journey:

Distance travelled$=AB$

Speed$=50\ km/h$

Therefore, time$=\frac{distance}{time}$

$=\frac{AB}{50}\ h$

Therefore, total distance travelled $=AB+AB=2AB$

Total time taken $=\frac{AB}{30}+\frac{AB}{50}$

$=\frac{5AB+3AB}{150}\ h$

$=\frac{8AB}{150}\ h$

$=\frac{4}{75}AB\ h$

Therefore, Average speed of the car $=\frac{total\ distance}{total\ time}$

$=\frac{2AB}{\frac{4}{75}AB}$

$=\frac{2\times75}{4}\ km/h$

$=37.5\ km/h$

Therefore, the average speed of the car is $37.5\ km/h$.

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Updated on: 10-Oct-2022

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