Rule  Description 

1  Average speed = \[\frac{\text{Total Distance}}{\text{Total time}}\] 
2  While traveling a certain distance d, if a man changes his speed in the ratio m : n, then the ratio of time taken becomes n : m. 
3  If a certain distance d, from A to B, is covered at a km/hr and the same distance is covered again from B to A in b km/hr, then the average speed during the whole journey is given by: Average speed = \[\frac{2ab}{a+b}\] km/hr. 
4  If t_{1} and t_{2} is time taken to travel from A to B and B to A respectively, the distance d from A to B is given by : \[d=(t_1 t_2 )\left(\frac{ab}{a+b}\right)\] 
5  If first part of the distance is covered at the rate of v_{1} in time t_{1} and the second part of the distance is covered at the rate of v_{2} in time t_{2}, then the average speed is \[\left(\frac{v_1t_1+v_2t_2}{t_1+t_2}\right)\] 
Rule  Description 

1 

2  If two persons start at the same time in opposite directions from two points A and B, and after crossing each other they take x and y hours respectively to complete the journey, then \[\frac{\text{Speed of first}}{\text{Speed of second}}=\sqrt{\frac{y}{x}}\] 
3  If a man changes his speed to \[\frac{a}{b}\] of his usual speed, reaches his destination late/earlier by t minutes then, usual time = \[\frac{t}{\left(\frac{b}{a}1\right)}\] 
4  A man covers a certain distance D. If he moves S_{1} speed faster, he would have taken t time less and if he moves S_{2} speed slower, he would have taken t time more. The original speed is given by: \[\frac{2\left(S_1\times S_2\right)}{S_2S_1}\] 
5  If a person with two different speeds U & V cover the same distance, then required distance:
(OR) 
6  A policemen sees a thief at a distance of d. He starts chasing the thief who is running at a speed of ‘a’ and policeman is chasing with a speed of ‘b’. In this case, the distance covered by the thief when he is caught by the policeman, is given by: \[d\left(\frac{a}{ba}\right)\] 
7  A man leaves a point A at t_{1} and reaches the point B at t_{2}. Another man leaves the point B at t_{3} and reaches the point A at t_{4}, then they will meet at: \[t_1+\frac{\left(t_2t_1\right)\left(t_4t_1\right)}{\left(t_2t_1\right)\left(t_4t_3\right)}\] 
8  Relation between time taken with two different modes of transport: \[t_{2x}+t_{2y}=2\left(t_x+t_y\right)\] where,

Rule  Description 

1  Time taken by a train to cross a pole = \[\frac{\text{Length of train}}{\text{Speed of train}}\] 
2  Time taken by a train to cross platform = \[\frac{\text{length of train + length of platform}}{\text{Speed of train}}\] 
3  When two trains with lengths L_{1} and L_{2} and with speeds S_{1} and S_{2} respectively, then (a) When they are moving in the same direction, time taken by the faster train to cross the slower train = \[\frac{L_1 + L_2}{\text{Difference of their speeds}}\] 
4  (b) When they are moving in the opposite direction, time taken by the faster train to cross each other = \[\frac{L_1 + L_2}{\text{Sum of their speeds}}\] 
5  Suppose two trains of lengths x km and y km are moving in the same direction at u km/hr and v km/hr respectively, then

6  Suppose two trains of lengths x km and y km are moving in opposite direction at u km/hr and v km/hr respectively, then

7  If a man is running at a speed of u m/sec in the same direction in which a train of length L meters is running at a speed v m/sec, then

8  If a man is running at a speed of u m/sec in a direction opposite to that in which a train of length L meters is running at a speed v m/sec, then

9  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. Then, A’s speed : B’s speed = \[\left(\sqrt{b}:\sqrt{a}\right)\] 
10  If a train of length L m passes a platform of x m in t_{1} seconds, then time taken t_{2} by the same train to pass a platform of length y m is given as \[t_2=\left(\frac{L+y}{L+x}\right)t_1\] 
11  From stations P and Q, two trains start moving towards each other with the speeds a and b, respectively. When they meet each other, it is found that one train covers distance d more than that of another train. In such cases, distance between stations P and Q is given as \[\left(\frac{a+b}{ab}\right)\times d\] 
12  The distance between two stations P and Q is d km. A train with speed a km/h starts from station P towards Q and after a difference of t hr another train with b km/h starts from Q towards station P, then both the trains will meet at a certain point after time T. Then,

13  The distance between two stations P and Q is d km. A train starts from P towards Q and another train starts from Q towards P at the same time and they meet at a certain point after t h. If the difference between the two trains is x km/h, then

14  A train covers distance d between two stations P and Q in t_{1} h. If the speed of train is reduced by a km/h, then the same distance will be covered in t_{2} h.
