# Quantitative Aptitude Notes : Time, Speed and Distance

Time, Speed & Distance is one of the most important topics in quantitative aptitude section in various SSC and Banking exams. In this blog post, we will cover all the important aspects of this topic.

###### Relationship Between Speed, Time & Distance

Speed = Distance / Time

We can deduce the following from this formula:-

– When time is constant, distance covered is directly proportional to the speed.
– When distance is the same, speed is inversely proportional to time.
###### Average Speed
Average Speed = Total Distance Traveled / Total Time Taken
– Remember that average speed is NOT the arithmetic mean of the speeds.
– Also, average speed can never be double or more than double of any of the original speeds.
###### Relative Speed
When two objects with speed S1 and S2 respectively and they are traveling in:
– Same direction, the relative speed (S’) is the difference of the individual speeds
S’ = S1 – S2
– Opposite direction, the relative speed (S’) is the sum of the individual speeds
S’ = S1 + S2
###### Trains Crossing
If L1 and L2 are the lengths of two trains moving at speeds V1 and V2 respectively, then the time taken by them to cross each other given by,
Time to Cross = ( L1 + L2 ) / (Relative Speed)
###### Boats & Streams
If a boat traveling at the speed (B) is in a stream, the speed of which is denoted by S and it is traveling:
– Upstream (against the direction in which the stream is flowing)
Upstream Speed = B – S
– Downstream (in the same direction as that of the flow of the stream)
Downstream Speed = B+ S
###### Circular Motion
– When two runners are on the same circular track, the time taken for them to meet for the first time is given by the following expression:-
Length of the track / Relative speed of the runners

– Number of times two runners meet on the circular track = Number of rounds gained by faster

runner over the slower one.

– If ratio of speeds of two runners running in circular track is x : y, they will meet at the starting point again in the time given by the following expressions:-

|x – y| time (if running in the same direction)
(x + y) time (if running in the opposite direction)
###### Questions on Races
Some points to remember while solving questions based on these are as follows:-
– the distance covered by the winner = length of the race
– loser’s distance = winner’s distance – (beat distance + start distance)
– winner’s time = loser’s time – (beat time + start time)

– if a race ends in a deadlock, i.e. both reach the winning post together then beat time = 0 and beat distance = 0

Hope this helps.
All the best!