Average speed= $$\frac{Total Distance Travelled}{Total Time Taken}$$
If a part of a journey is travelled at speed $$S_{1}$$ km/hr in $$T_{1}$$ hours and the remaining part at speed $$S_{2}$$ km/hr in $$T_{2}$$ hours then.
Total distance travelled= $$S_{1}T_{1}$$+$$S_{2}T_{2}$$ km
Average speed=$$\frac{S_{1}T_{1}+S_{2}T_{2}}{T_{1}+T_{2}}$$ km/hr
If $$D_{1}$$ km is travelled at speed of $$S_{1}$$ km/hr, and $$D_{2}$$ km is travelled at speed of $$S_{2}$$ km/hr then
Average Speed= $$\frac{D_{1}+D_{2}}{\frac{D_{1}}{S_{1}}+\frac{D_{2}}{S_{2}}}$$ km/hr
- In a journey travelled at different speeds, if the distance covered in each stage is constant, the average speed is the harmonic mean of the different speeds.
- Suppose a man covers a certain distance st x km/hr and an equal distance at y km/hr
Then the average speed during the whole journey is $$\frac{2xy}{x+y}$$ km/hr
- In a journey travelled with different speeds, if the time travelled in each stage is constant, the average speed is the arithmetic mean of the different speeds.
- If a man travelled for a certain time at the speed of x km/hr and travelled for an equal amount of time at the speed of y km/hr then
Then the average speed during the whole journey is $$\frac{x+y}{2}$$ km/hr
