Time, Speed & Distance

(ii) Time =

(iv) x km/hr = (x × ) m/sec.

(vi) If a certain distance is covered at x km/hr and the same distance covered at y km/hr, then the average speed during whole journey = km/hr.

(i) Time taken by a train x meters long in passing a signal post or a pole or a standing man is the same as the time taken by the train to cross 'x' meters with its own speed.

(iii) Suppose two trains or bodies are moving in the same directions at 'u' km/hr and 'v' km/hr such that u > v, then their relative speed = (u - v) km/hr.

(v) Suppose two trains or bodies are moving in the opposite directions at 'u' km/hr and 'v' km/hr. Then, relative speed = (u + v) km/hr.

(vii) If two trains start at the same time from stations A and B towards each other and after crossing, they take 'a' & 'b' hours in reaching B and A respectively. Then,
A's speed : B's speed = ().

Example: A train 100 m long is running with a speed of 70 km/hr. In what time will it pass a man who is running at 10 km/hr in the same direction in which the train is going?

Speed of train relative to man = (70 - 10) kmph =.
Time taken by the train to cross the man
= Time taken by it to cover 100 m at= 6 sec. (Boats & Streams)
Let the speed of a boat in still water be x km/hr and the speed of the stream be y km/hr. Then:


Example: A man can row upstream at 8 km/hr and downstream at 10.6 km/hr. Find man's speed in still water and the rate of the current.

Rate in still water = (8 + 10.6) km/hr = 9.3 km/hr
Rate of current = (10.6 - 8) km/hr = 1.3 km/hr.
Example A man can row 6 kmph in still water. It takes him twice as long as to row up the river as to row down the river. Find the rate of stream.

Let man's rate upstream = x km/hr Then, man's rate downstream = 2x km/hr
? Man's rate in still water = (x + 2x) km/hr ? = 6 ? x = 4
? Rate of upstream = 4 km/hr, Rate downstream = 8 km/hr
? Rate of current = (8 - 4) km/hr = 2 km/hr

Points to remember:
(1) Speed & Distance are directly proportional. So if the speed is doubled the distance traveled is also doubled (Time is constant).
(2) Distance and time are directly proportional. If distance to be traveled is tripled, then the time taken would also be tripled (Speed is constant).

- The time is inversely related to the speed.
- If the distance remains same and speed doubles then the time taken to travel that distance becomes 1/2 times the original time taken at the original speed.
- Similarly if the time taken to travel the same distance has become 5 times the original time then we can conclude that the speed must have become 1/5th of the original speed.

Also Remember:
(i) If two objects are moving in opposite directions towards each other or away from each other on a straight line at speeds U & V, then they seem to be moving towards each other or away from each other at a relative speed = (speed of 1st) + (speed of 2nd) = U + V.
(ii) If two men move in the same direction with speeds U and V, then relative speed = difference of their speeds i.e., U - V.
(iii) If a man and train are running simultaneously at 'm' & 't' - may be in the compartment or on the ground - assume the man is stationary and speed of the train is 'm + t' if man is running opposite and 'm-t' if running in the same direction.
(iv) Whether the two trains are moving in the same direction or in the opposite direction the total distance required to be traveled before they cross each other completely = sum of the lengths of the two trains. And this distance is to be covered at the relative speeds of the train.
(v) Problems in a circular motion make use of both the relative speed and the LCM concept.
(vi) The number of rounds the faster person makes is always one round more than the slow runner whenever and wherever they meet for the first time.
(vii) Moving at X kmph means moving at X.5/18 m/sec.