Education & Learning: Institute of Hotel Management Bhubaneswar Course Guide Education & Learning: Legal Aptitude Practice Quiz 16 Education & Learning: IPU LLB Exam Important Dates Education & Learning: Hotel Management Entrance Exams After Class 12 Education & Learning: DU LLB Entrance Exam Syllabus for 2018 Education & Learning: IPU CET B.Com Result 2020 Education & Learning: Christ University Law Admission 2018 Eligibility Criteria Education & Learning: Institute of Hotel Management Lucknow Course Guide
Equal Justice Films Author
Published: July 22, 2026
Read: 4 min
In: Education & Learning

Time Speed and Distance

Your ability to solve the problems on relative motion, circular motion, and problems
based on trains, boats, clock, races etc. will depend only on the depth of your
understanding
1. Speed Distance/Time
2. Distance = Speed x Time
3. Time = Distance/ Speed
4. x km/hr = (x x 5/18) m/sec
5. y m/sec = (y x 18/5) km/hr
6. If a certain distance is covered at x km/hr and the same distance is covered at
y km/hr, then the average speed during the whole journey = km/hr
7. If a person changes his speed in the ratio m: n. then the ratio of time taken
becomes n : m
8. For the same distance speed varies inversely as time and in the same time
distance varies directly as speed
9. Average Speed =
Please note that the average speed of a moving body is NOT EQUAL to the average
of the speed
10. If a body covered one part of the journey at speed p and the remaining part of
the journey at speed q and the distances of the two parts of the journey are in the
ratio m : n, then the average speed for the entire journey is
Conversions
  • To convert cm to metre divide by 100.
  • To convert km to min. multiply by 1000.
  • To convert hours to min. multiply by 60.
  • To convert hours to sec multiply by 3600.
  • To convert minutes to hours divide by 60.
  • To convert seconds to hours divide by 3600.
Example 1.Time taken at 48 km/h is 24 minutes. What is the time if speed
decreases by 25%?
Solution:Speed ratio = 4: 3
Time ratio 3: 4 = 24: 32
Time ratio = 32 minutes

Example 2. Walking at 48% less speed, time taken is 75 minutes. Find the time
taken a usual speed.
Solution:Speed ratio = 100 : 52 25 : 13
Time ratio = 13 : 25 (speed and time vary inversely)
= 39 : 75
Time = 39 minutes
Example 3.A 240m long train travelling at 36 km/h clears a 600 m long platform in
how much time.
Solution: Speed of Train = 36 x 5/18 m/s 10m/sec.
Time = Distance/Speed 840m/10m/s = 84sec.
Example 4. A train at 148 km/h .overtakes a motorcyclist at 58 km/h in the same direction in 10 sec. What is the length of the train?
Solution:Distance = Speed x time
= (148 – 58) x 5/18 x 10m 250m
Example 5.Speed from A to B = 10 km/h and from B to A is 40 km/h. What is the average speed?
Solution:Average Speed = 2 x 10 x = 16 km/hr.
(If the distance is same then average speed is the harmonic mean)

Trains

Relative Speed:

The speed of one (moving) body in relation to another moving body is called the
relative speed of these two bodies, i.e., it the speed of one moving body as
observed, from the second moving body.
If two bodies are moving in the same direction, the relative speed is equal to the
difference of the speed of the two bodies.
If two bodies are moving in the opposite direction, the relative speed is equal to the
sum of the speeds of the two bodies.
  • When a train crosses a tree/pole etc. Time taken to cross in seconds x speed in m/s = length of the train in m.
  • When a train crosses a platform/tunnel/bridge etc. Time taken to cross in seconds x speed in m/s = length of the train in m + length of platform/tunnel/bridges in m.
  • In problems on two trains the lengths of the trains are always added irrespective of whether the trains are running in same or opposite directions on parallel tracks.
  • If trains are running in opposite directions.
         Time taken to completely cross each other =
  • If trains are running in same directions
         Time taken by faster train to completely overtake the slower train
              =
  • If two objects pass each other while travelling in the same direction then the
                time taken to pass =

Example 1.What is the time taken by a train running at 72 km/hr to cross a man
standing on a platform, the length of the train being 180 m?
Solution: Speed of train = 72 kmph = 72 x = 20 m/s
Distance = length of the train = 180 m
Time = = 9 sec


Example 2. How long will a train 100m long and traveling at a speed of 45 kmph,
take to cross a platform of length 250 m?
Solution: Distance = length of the train + length of the platform = 100 + 250 = 350m
Speed of the train = 45 kmph
= 45 x = 12.5 m/sec.
Therefore, Time = = 28 sec.


Example 3. Find the length of bridge, which a train 120 m long traveling at 54 kmph
can cross in 30 seconds.
Solution: Speed of the train = 54 kmph = 54 x = 15 m/sec
Distance covered in 30 seconds = 15 x 30 = 450 m
Length of bridge = Distance covered — Length of the train = 450 – 120 = 330 m.

Boat and Stream

Problems related to boats and streams are different in the computation of relative
speed from those of train/cars.
When a boat is moving in the same direction as the stream or water current, the
boat is said to be moving
WITH THE STREAM OR CURRENT.
When a boat is moving in a direction opposite to that of the stream or water current,
it is said to be moving