Speed, journey time and average speed

At constant speed, \(d=vt\), \(v=\dfrac dt\) and \(t=\dfrac dv\). Over a complete journey, average speed is total distance divided by total elapsed time, including stops within that journey.

Example

A vehicle travels \(60\text{ km}\) at \(40\text{ km/h}\), stops for \(30\) minutes, then travels \(60\text{ km}\) at \(60\text{ km/h}\).

\(\text{Total time}=\dfrac{60}{40}+\dfrac{30}{60}+\dfrac{60}{60}=3\text{ h}\).

\(\text{Average speed}=\dfrac{120}{3}=40\text{ km/h}\). Departing at 08:40, it arrives at 11:40.

Without the stop the average would be \(48\text{ km/h}\), not \(50\text{ km/h}\). A simple average of two speeds applies only when the travelling times at those speeds are equal.