A car covers $$\frac{1}{5}$$  of the distance from A to B at the speed at 8 km/hr, $$\frac{1}{10}$$ of the distance at 25 km per hour and the remaining at the speed of 20 km per hour. Find the average speed of the whole journey.

$$ average speed = \frac{total distance}{total time} $$

let the total distance be d

time taken by the car to cover $$\frac{1}{5}$$ of the distance from A to B at the speed at 8 km/hr, t1 = $$ \frac{\frac{d}{5}}{8} = \frac{d}{5 \times 8} = \frac{d}{40} $$

time taken by the car to cover $$\frac{1}{10}$$ of the distance at 25 km per hour, t2 = $$ \frac{\frac{d}{10}}{25} = \frac{d}{25 \times 10} = \frac{d}{250} $$

time taken by the car to cover remaining at the speed of 20 km per hour t3

remaining distance = $$ 1 - (\frac{1}{5} + \frac{1}{10}) = \frac{7}{10} $$

$$ t3 = \frac{\frac{7d}{10}}{20} = \frac{7d}{200} $$

$$ average speed = \frac{d}{t1 + t2 + t3} $$

                           = $$ \frac{d}{\frac{d}{40} + \frac{d}{250} +  \frac{7d}{200}} $$

                           = $$ \frac{d}{\frac{25d + 4d + 35d}{1000}}= \frac{d \times 1000}{64d} = 15.625 $$