A car moves with a speed of $30\ km/h^{-1}$ for half an hour, $25\ km/h^{-1}$ for one hour and $40\ km/h^{-1}$ for two hours. Calculate the average speed of the car.

For the first part of the journey:

Speed$=30\ km/h$

Time $=\frac{1}{2}\ h$

Therefore, the $distance_1=speed\times time$

$=30\ kmh^{-1}\times \frac{1}{2}\ h$

$=15\ km$

For second part of the journey:

Speed$=25\ kmh^{-1}$

Time $=1\ h$

$distance_2=25\ kmh^{-1}\times1\ h$

$=25\ km$

For the third part of the journey:

Speed $=40\ km/h^{-1}$

Time $=2\ h$

$distance_3=speed\times time$

$distance_3=40\ km/h^{-1}\times 2\ h$

$=80\ km$

Therefore, total distance$=disstance_1+distance_2+distance_3$

$=15\ km+25\ km+80\ km$

$=120\ km$

Total time taken $=\frac{1}{2}\ h+1\ h+2\ h$

$=\frac{7}{2}\ h$

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

$=\frac{120\ km}{\frac{7}{2}\ h}$

$=34.28\ km/h$