19 Nov 2015

PrepHelp Educators

Solving Problems on Speed, Time and Distance

Speed, time and distance Based problems are Frequently asked in CAT,CSAT,SSC,Banking and various other competition exams. So it becomes necessary for us to learn this topic. We will move with this topic from the basics.


Speed of a vehicle is defined as the distance covered by that vehicle in total time.

Speed = Distance/time


Generally in exams of SSC, Banking questions on speed, time and distance are very easy as compared to CAT and various other Management Exams ranging from SNAP,NMAT etc.

Questions Asked in SSC Are Having a Statement like

Q. A person moves a distance of 5 km at a speed of 10km/hr by foot and then he hired a cab for a distance of 15km at a speed  of 45 km/hr then he boarded on a train for a distance of 100km at speed of 50km/hr. find the average speed of that person?

A. In order to solve this type of Problem first we should keep this in our mind that average speed = Total Distance travelled/Total time taken to travel that distance.

So, Let us start solving this problem Total Distance Travelled by the person = (5+15+100)km = 120km.

Time Taken by the person to move that distance = for finding the time taken we need to find individual time taken by to person on moving by foot, travelling in cab and finally in train.

For that We will use the formula  time = Distance/Speed.

Time taken by him will be = 5/10 + 15/45 + 100/50 = 17/6hr.

Average Speed = Total Distance/Total Time.

Av. speed= 120x6/17 =   42.35km/hr. is our answer


Another type of problem that can be asked in the exam are based on Boats and streams. For solving this type of problem some Key Points should be understood that are

Speed of Stream = Speed of stream is the called the speed of the water at which it is flowing. Let us name this speed as 'U km/hr.'

Speed of Boat = Speed of Boat is know as the speed at which the boat can move in steady water. Let us name this speed as 'V km/hr.'


When a boat moves down stream the speed of the boat 'V km/hr.' get increased because the speed of the stream get added to the speed of the Boat

So in this case the speed of the moving boat will become 'V+U km/hr.'

while solving any problem based on the boat which is moving down stream we will use the speed as "V+U km/hr."


When a boat moves up the stream the speed of the boat get decreased because of the friction applied by the stream on that boat so that speed of the stream get subtracted from the speed of the boat.

ie. Speed Becomes " V-U km/hr."

While solving any problem based on the boat moving up stream we will use the speed as " V-U km/hr."

Now let us use the above formulae in solving the problems.

Q. A boat moves a distance downstream and returns the same distance upstream its average speed for the whole journey was 3 km/hr. if the speed of the boat be 4km/hr. find the speed of stream?

A. As we have already discussed the speed of boat in downstream is = 4+s (s=speed of stream)

Speed of Boat in Upstream =4-s

LET x be the distance traveled upstream and Down stream so total distance =2x km.

Time for upstream = x/(4-s)

Time in down stream = x/(4+s)

Total Time = x{8/(16-s^2)}

Average Speed= Total Distance/Total Time taken

So solve this Problem. Answer for this Problem is 2km/hr.

 Relative Speed

Case 1:

Two bodies are moving in opposite directions at speed V1 & V2 respectively. The relative speed is defined as Vr=V1+V2

Case 2:

Two bodies are moving in same directions at speed V1 & V2 respectively. The relative speed is defined as Vr=|V1V2|

 Train Problems

The basic equation in train problem is the same Speed=Distance/Time

The following things need to be kept in mind while solving the train related problems.

  • When the train is crossing a moving object, the speed has to be taken as the relative speed of the train with respect to the object.

  • The distance to be covered when crossing an object, whenever trains crosses an object will be equal to: Length of the train + Length of the object

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