About Speed Distance & Time
About Speed Distance & Time
Aptitude & Reasoning
11 min read
Speed, distance, and time are closely related concepts used to describe motion. Whether a person is walking to work, a car is travelling between cities, a train is passing a platform, or two vehicles are moving toward each other, the same fundamental mathematical relationships can be used to analyse the journey.
The Speed, Distance & Time topic is one of the most important areas of quantitative aptitude. It frequently appears in school mathematics, entrance tests, recruitment examinations, banking exams, competitive tests, and general aptitude assessments.
At its simplest, the topic is based on one relationship:
Speed = Distance ÷ Time
From this formula, distance and time can also be calculated. However, more advanced questions may involve average speed, relative speed, trains, races, changing speeds, stops, unit conversion, circular tracks, and multi-stage journeys.
The key to solving these questions effectively is not memorizing dozens of formulas. It is understanding how speed, distance, and time relate to one another.
Understanding Speed
Speed tells us how quickly an object covers distance.
If a car travels 120 kilometres in 2 hours, its average speed is:
120 ÷ 2 = 60 km/h
Speed is therefore calculated as:
Speed = Distance ÷ Time
Common units include:
kilometres per hour (km/h)
metres per second (m/s)
miles per hour (mph)
The unit matters because distance and time must be compatible before performing calculations.
For example, metres should normally be paired with seconds, while kilometres are commonly paired with hours.
Understanding Distance
Distance describes how far an object travels.
If speed and travel time are known, distance can be calculated using:
Distance = Speed × Time
For example, a bus travelling at 50 km/h for 3 hours covers:
50 × 3 = 150 km
Distance questions are usually straightforward when speed remains constant.
More complex problems may divide the journey into several stages with different speeds or travel times.
In those situations, calculate the distance for each stage separately before combining them.
Understanding Time
If distance and speed are known, travel time can be calculated using:
Time = Distance ÷ Speed
Suppose a vehicle must travel 180 kilometres at 60 km/h.
The required time is:
180 ÷ 60 = 3 hours
Time questions become more complicated when speeds change during the journey or when stops are included.
Carefully determine whether the question asks for travel time or total elapsed time, because waiting periods may affect one but not the other.
The Speed–Distance–Time Triangle
A useful way to remember the three basic formulas is the speed-distance-time triangle.
Place distance at the top and speed and time at the bottom:
Distance
Speed × Time
Cover the quantity you want to calculate.
To find distance:
Speed × Time
To find speed:
Distance ÷ Time
To find time:
Distance ÷ Speed
Although this memory technique is useful for beginners, understanding the relationship is more important than relying entirely on the triangle.
Converting km/h to m/s
Many aptitude questions require converting between kilometres per hour and metres per second.
The standard conversion is:
1 km/h = 5/18 m/s
Therefore, to convert km/h to m/s:
Multiply by 5/18
For example:
72 km/h × 5/18 = 20 m/s
This conversion is particularly important in train problems, where train lengths may be provided in metres while speeds are given in kilometres per hour.
Using inconsistent units is one of the most common causes of incorrect answers.
Converting m/s to km/h
To convert metres per second into kilometres per hour:
Multiply by 18/5
For example:
20 m/s × 18/5 = 72 km/h
The two conversions are therefore opposites:
km/h → m/s: multiply by 5/18
m/s → km/h: multiply by 18/5
Recognizing these conversions quickly can save valuable time in aptitude examinations.
Average Speed
Average speed is frequently misunderstood.
The correct formula is:
Average Speed = Total Distance ÷ Total Time
It is not always the simple average of two speeds.
Suppose a vehicle travels 100 km at 50 km/h and another 100 km at 100 km/h.
The first part takes:
100 ÷ 50 = 2 hours
The second part takes:
100 ÷ 100 = 1 hour
Total distance = 200 km
Total time = 3 hours
Average speed:
200 ÷ 3 ≈ 66.67 km/h
Simply averaging 50 and 100 would give 75 km/h, which is incorrect.
Equal-Distance Average Speed
A useful shortcut exists when the same distance is travelled at two different speeds.
If the speeds are a and b, the average speed is:
2ab ÷ (a + b)
For speeds of 50 km/h and 100 km/h:
2 × 50 × 100 ÷ 150
= 66.67 km/h
This shortcut works only when the distances travelled at the two speeds are equal.
It should not be applied automatically to every average-speed question.
Relative Speed
Relative speed describes how quickly the distance between two moving objects changes.
If two objects move toward each other:
Relative Speed = Speed 1 + Speed 2
For example, two cars approaching each other at 60 km/h and 40 km/h have a relative speed of:
60 + 40 = 100 km/h
If two objects move in the same direction:
Relative Speed = Difference between their speeds
If one car travels at 80 km/h and another at 60 km/h in the same direction, their relative speed is:
80 − 60 = 20 km/h
Relative speed is essential for solving meeting, overtaking, and train problems.
Two Objects Moving Toward Each Other
Suppose two cities are 300 kilometres apart.
One vehicle leaves City A at 70 km/h while another leaves City B at 80 km/h, both travelling toward each other.
Their combined relative speed is:
70 + 80 = 150 km/h
Time until they meet:
300 ÷ 150 = 2 hours
These problems become more difficult when vehicles begin at different times, but the underlying principle remains the same.
Determine how much distance remains when both are moving, then use relative speed.
Overtaking Problems
When two vehicles travel in the same direction, the faster vehicle gains on the slower one at their difference in speed.
Suppose one vehicle travels at 90 km/h and another at 70 km/h.
Relative speed:
90 − 70 = 20 km/h
If the faster vehicle begins 40 kilometres behind, the time required to catch the slower vehicle is:
40 ÷ 20 = 2 hours
Overtaking problems involving trains use the same principle but also require considering the lengths of the trains.
Train Passing a Person or Pole
Train questions are a classic part of speed-distance-time aptitude.
When a train passes a stationary person, pole, or signal, it must travel a distance equal to its own length.
Therefore:
Time = Train Length ÷ Train Speed
Suppose a 200-metre train travels at 20 m/s.
Time to pass a pole:
200 ÷ 20 = 10 seconds
The critical step is ensuring that the train's speed and length use compatible units.
Train Passing a Platform
When a train passes a platform, the entire train must clear the entire platform.
Therefore, the total distance travelled is:
Train Length + Platform Length
If a 150-metre train passes a 250-metre platform:
Total distance = 400 metres
If its speed is 20 m/s:
Time = 400 ÷ 20 = 20 seconds
The same principle applies when a train passes a bridge or tunnel.
Two Trains Crossing Each Other
When two trains completely cross each other, the total distance is the sum of their lengths.
If they travel in opposite directions, add their speeds.
If they travel in the same direction, subtract their speeds.
For example, suppose two trains are 120 metres and 180 metres long.
Total distance:
120 + 180 = 300 metres
If they move toward each other at 15 m/s and 10 m/s:
Relative speed:
15 + 10 = 25 m/s
Time to cross:
300 ÷ 25 = 12 seconds
Race Problems
Speed-distance-time principles also apply to races.
Questions may compare runners based on:
Distance advantages
Time advantages
Speed ratios
Finishing positions
Suppose A runs 100 metres in 10 seconds while B requires 12.5 seconds.
A's speed is:
100 ÷ 10 = 10 m/s
B's speed is:
100 ÷ 12.5 = 8 m/s
When A finishes 100 metres, B will have covered:
8 × 10 = 80 metres
Therefore, A beats B by 20 metres.
Race questions often become easier when speeds are converted into ratios.
Speed Ratios and Time Ratios
For the same distance, speed and time are inversely proportional.
If one person moves twice as fast as another, that person requires half as much time to cover the same distance.
Therefore:
Speed Ratio = Inverse of Time Ratio
If speeds are in the ratio:
2 : 3
Then the times required for the same distance are:
3 : 2
This relationship is useful for solving many aptitude questions without calculating actual distances.
Changing Speed During a Journey
Many problems divide a journey into multiple sections.
For example, a traveller might cover:
100 km at 50 km/h
then
120 km at 60 km/h.
Calculate each travel time:
100 ÷ 50 = 2 hours
120 ÷ 60 = 2 hours
Total distance = 220 km
Total time = 4 hours
Average speed = 55 km/h
Treating each part separately helps prevent mistakes.
Stops and Effective Speed
Some vehicles stop during a journey.
For example, a bus may travel at 60 km/h while moving but stop for 10 minutes every hour.
Its effective average speed over the full elapsed time will therefore be lower than 60 km/h.
Questions may distinguish between:
Running speed — speed while the vehicle is moving.
Average or effective speed — total distance divided by total elapsed time, including stops.
Read the wording carefully to determine whether stopping time should be included.
Boats and Streams
Boat-and-stream problems are closely related to speed-distance-time.
A boat moving downstream receives assistance from the current:
Downstream Speed = Boat Speed + Stream Speed
Moving upstream:
Upstream Speed = Boat Speed − Stream Speed
If downstream and upstream speeds are known:
Boat Speed in Still Water = (Downstream + Upstream) ÷ 2
Stream Speed = (Downstream − Upstream) ÷ 2
Although boats and streams are sometimes treated as a separate aptitude topic, they rely directly on relative-speed principles.
Circular Track Problems
When two people travel around a circular track, they may meet repeatedly.
If they move in opposite directions, their relative speed is the sum of their speeds.
If they move in the same direction, use the difference.
The time required for the faster person to gain one full lap on the slower person can be calculated using:
Track length ÷ relative speed.
More advanced problems may ask when several runners return to their starting point together, which can involve concepts such as least common multiples.
Time Saved by Increasing Speed
A common aptitude question states that a person would arrive a certain amount of time earlier by travelling faster.
These problems often require comparing two travel times.
For the same distance:
Distance / Original Speed − Distance / New Speed = Time Saved
This equation can be used to find an unknown distance or speed.
Rather than trying to memorize a special formula, form the relationship directly from:
Time = Distance ÷ Speed.
Late and Early Arrival Problems
Another common question type involves someone arriving late at one speed but early at another.
For example:
At 30 km/h, a person arrives 10 minutes late.
At 40 km/h, the person arrives 5 minutes early.
The difference between the two journey times is therefore:
10 + 5 = 15 minutes.
This difference can be combined with the two speed equations to determine the journey distance or scheduled travel time.
The key is recognizing that "late" and "early" refer to the same scheduled arrival time.
Common Mistakes in Speed, Distance & Time Problems
Many errors come from interpretation rather than difficult mathematics.
Common mistakes include:
Mixing kilometres with metres
Mixing hours with seconds
Averaging speeds incorrectly
Adding speeds when objects move in the same direction
Forgetting train length
Ignoring platform or bridge length
Including or excluding stops incorrectly
Confusing speed with velocity
Using total time incorrectly in multi-stage journeys
Checking units before calculating prevents many of these errors.
How to Solve Questions Faster
For aptitude exams, use a consistent approach.
First, identify what the question asks.
Then write down the known:
Speed — Distance — Time
Convert units immediately if necessary.
Determine whether the problem involves:
Basic motion
Average speed
Relative speed
A train
A race
Multiple stages
Stops
A circular track
Use ratios when they simplify the calculation.
Avoid unnecessary decimal calculations when fractions provide a cleaner solution.
Finally, check whether the answer is reasonable. A journey cannot normally take less time after speed decreases unless another condition has changed.
Why Speed, Distance & Time Matters
These concepts are useful far beyond aptitude examinations.
Travel planning uses distance and expected speed to estimate arrival times.
Transport companies use similar calculations when scheduling vehicles.
Athletes analyse pace and speed.
Engineers study motion.
Navigation systems estimate journey duration based on distance and changing speeds.
Logistics companies use travel-time models to plan routes and deliveries.
Understanding the basic relationship between speed, distance, and time therefore provides a practical foundation for many real-world calculations.
Test Your Speed, Distance & Time Skills
Can you calculate how long two vehicles take to meet? Can you determine the time required for a train to cross a platform? Do you know why the average of two speeds is not always the average speed?
The Speed, Distance & Time quizzes cover basic formulas, unit conversion, average speed, relative speed, trains, races, overtaking, multi-stage journeys, circular tracks, travel-time differences, and other quantitative aptitude problems.
Questions can range from simple formula applications to multi-step problems requiring careful interpretation and efficient calculation.
Whether you are preparing for an aptitude exam, competitive examination, recruitment test, or simply want to strengthen your numerical reasoning, this topic provides practical exercises for improving both speed and accuracy.