Speed, Time and Distance

The questions on speed, time and distance are based on one general formula:

The Concept
There are three parameters: Speed, Time and Distance. Keeping one parameter constant and changing another, the third parameter also gets changed.

Example: Suppose you travel from your office (A) to your home (B). The distance between A and B is 30 km. You travel at the speed of 40 km/hr and it takes 45 minutes.

Boats and Streams

In water or river, the direction along the stream is called downstream. Direction against the stream is called upstream.
If the speed of boat in still water is U km/hr and the speed of stream is V km/hr, then

• speed downstream = (U + V) km/hr
• speed upstream = (U - V) km/hr

If the speed downstream is A km/hr and the speed upstream is B km/hr, then

• Speed of boat in still water = 1/2(A+B) km/hr
• Rate of stream or river = 1/2(A-B) km/hr

Trains

A train has a definite length. The distance covered by the train depends on the length of the train.

1. Time taken by a train x mt long in passing a stationary point (it can be a signal post or a pole or a standing man) is equal to time taken by the train to cover x mt.
2. Time taken by a train x mt long in passing a stationary object of length y mt is equal to time taken by the train to cover (x+y) mt.
3. Suppose two trains are moving in the same direction at u kmph and v kmph such that u > v, then their relative speed is u-v kmph.
4. Suppose two trains are moving in opposite direction at u kmph and v kmph then, their relative speed is equal to (u+v) kmph.
5. If two trains of length x km and y km are moving in opposite diredtions at u kmph and v kmph, then time taken by the train to cross each other is equal to (x+y)/(u+v) hr.
6. If two trains start at the same time from 2 points A and B towards each other and after crossing they take a and b hours in reaching B and A respectively, then ratio of A's speed : B's speed = (b^1/2 : a^1/2).                      NEXT