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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$=\frac{total\ distance}{total\ time}$
$=\frac{120\ km}{\frac{7}{2}\ h}$
$=34.28\ km/h$