Two buses start at the same moment, one from Pune towards Solapur and the other from Solapur towards Pune, each running at a steady speed. They pass each other on the way, and after passing, the first reaches Solapur in 4 hours while the second reaches Pune in 9 hours. The ratio of the first bus's speed to the second's is:

Let them meet after $t$ hours. The stretch the first bus has already covered is what the second still has to do, so $v$₁$t=9v$₂; likewise $v$₂$t=4v$₁. Multiplying the two gives $t^2=36$, so $t=6$, and then $6v$₁ = $9v$₂ → $v$₁ : $v$₂ = 3 : 2. (In short the speeds go as √9 : √4. Quoting 9 : 4 uses the times themselves and forgets the square root, and it also has the ratio the right way up only by luck — the bus needing LESS time after the meeting is the faster one.)