A car complete the first half of its journey with speed `v_1`, and the rest half with speed `v_2`. The average speed of the car in whole journey:

Explanation

Let total distance covered in journey `= d`

Speed of car in first half covering distance `d/2 = v_1`

Time taken by the car during first half of the journey `(t_1)= (d/2)/(v_1) = d/(2v_1)`

Speed of car in second half covering distance `d/2 = v_2`

Time taken by the car during second half of the journey `(t_2)= (d/2)/(v_2) = d/(2v_2)`

`:.` Average speed ` = d/(t_1+t_2) = d/(d/(2v_1)+d/(2v_2))`

` =2/(1/v_1+1/v_2) = (2v_1v_2)/(v_1+v_2)`

So, average speed of the car is `(2v_1v_2)/(v_1+v_2)`.