**Very useful**

If Speeds forms an Arithmetic Progression, then time taken will be in Harmonic Progression (Constant distance)

If Time taken forms an AP, then speed forms an HP. (Again for constant distance)

Ex: CAT 2006 Question - Arun, Barun and Kiranmala start from the same place and travel in the same direction at speeds of 30,40 and 60 km per hour respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

Speeds are in HP and distance is constant. So time should be AP

t, t + 2 and ? should be in AP. So unknown = t + 4, and answer is Kiranmala started 4 hours after Arun.