A car travels the first one third of a certain distance with a speed of 10 km/hr, the next one third distance with a speed of 20 km/hr and the last one third distance with a speed of 60 km/hr. thee average speed of the car for the whole journey is :

Let the distance travelled by a car be x km
First $$\frac{x}{3}$$ km distance cover at speed of 10 km/hr
Second $$\frac{x}{3}$$ km distance cover at speed = 20 km/hr
Third $$\frac{x}{3}$$ km distance cover at speed = 60 km/hr
According to the question,
Total time ,
$$\eqalign{ & = \frac{x}{{3 \times 10}} + \frac{x}{{3 \times 20}} + \frac{x}{{3 \times 60}} \cr & = \frac{x}{{30}} + \frac{x}{{60}} + \frac{x}{{180}} \cr & = \frac{{6x + 3x + x}}{{180}} \cr & = \frac{{10x}}{{180}} \cr & = \frac{x}{{18}} \cr} $$
Average speed :
$$\eqalign{ & = \frac{{x \times 18}}{x}{\text{ km/hr}} \cr & = 18{\text{ km/hr}} \cr} $$