Time & Distance, Trains, Boats & Streams Tricks and Formulas

Time & Distance

Suppose a man covers a distance at ‘x’ kmph and an equal distance at ‘y’ kmph, and then average speed during his whole journey is [2xy/(x+y)] kmph


  • Lengths of trains are ‘x’ km and ‘y’ km, moving at ‘u’ kmph and ‘v’ kmph (where,u>v) in the same direction, then the time taken y the over-taker train to cross the slower train is [(x+y)/(uv)] hrs

  • Time taken to cross each other is[(x+y)/(u+v)] hrs

  • If two trains start at the same time from two points A and B towards each other and after crossing they take a and b hours in reaching B and A respectively.

  • xkmph=(x×5/18)m/sec.

  • ymetres/sec=(y×18/5)km/hr.

Boats & Streams

  • If the speed of a boat in still water is ukm/hr and the speed of the stream is v hm/hr , then: Speeddownstream=(u+v)km/hr.. and Speedupstream=(uv)km/hr.

  • If the speed downstream is a km/hr and the speed upstream is b km/hr, then: Speed in still water =½(a+b)km/hr . and Rate of stream =½(ab) km/hr.