Time and Distance: Formulas, Tricks, Speed and Examples

Time and Distance is one of the most common topics in quantitative aptitude. It is used in school mathematics, competitive exams, railway exams, banking exams, SSC, placement tests, and daily life problems. The topic is based on a simple relationship: speed tells how much distance is covered in a fixed time.

Most questions from this chapter use three quantities: speed, time, and distance. If any two are known, the third can be found. The difficulty comes from unit conversion, average speed, relative speed, trains crossing each other, and two persons moving in the same or opposite directions.

This updated post keeps the existing formulas and images already present in the article and adds detailed explanations, tables, solved examples, exam shortcuts, train cases, relative speed, practice questions, and FAQs. The aim is to make the page more complete and easier for students preparing aptitude topics.

Meaning of Time and Distance

Distance is the length of path covered by a moving object. Time is the duration taken to cover that distance. Speed is the rate at which distance is covered. If speed is high, less time is needed for the same distance. If speed is low, more time is needed.

For example, if a car travels 60 km in 2 hours, its speed is 30 km/h. If the same car travels at 60 km/h, it covers 120 km in 2 hours. These simple ideas are the base of all time and distance questions.

Important Terms

Term	Meaning
Speed	Distance covered per unit time
Distance	Total path covered
Time	Duration of journey
Average speed	Total distance divided by total time
Relative speed	Speed of one moving body with respect to another

Existing Time and Distance Formulas

$speed = \frac{distance}{time}$

$X km/hour = x * \frac{1000 metres}{60×60 second} = x*\frac{5}{18} m/sec$

If the ratio of the speed of A & B is a:b then the ratio of time taken by them to cover the same distance is $\frac{1}{a} :\frac{1}{b} = b:a$
“The time taken for covering a certain distance is increasingly proportional to the speed.”
Similarly time taken to finish a work is the inversed proportional to the number of working unit
When by A, cover a certain distance at x km/h & b cover the same distance at y km/h than the average speed of both during the whole journey
$journey = (\frac{2xy}{(x+y)})km/h$

Difference distance by two moving body in same direction with ‘u’ m/s and ‘v’ m/s
u>v then their relatives speed = (u-v) m/s
u>v in opposite direction they cross to each other = $\frac{(a+b)}{(u+v)} second$
(With length of a & b meter)
u>v in same direction cross to each other = $\frac{(a+b)}{(u-v)} second$
if two bodies start at the same time from station A & b to words each other . they have taken time a & b second to reaching A to B & B to A .
then A’s speed: √b:√a

Basic Formulas

Quantity	Formula
Speed	Distance / Time
Distance	Speed x Time
Time	Distance / Speed
Average speed	Total distance / Total time

These three formulas are enough for basic questions. The important part is to keep units same. If speed is in km/h, time should be in hours and distance should be in kilometres. If speed is in m/s, time should be in seconds and distance should be in metres.

Unit Conversion

Unit conversion is very important in this chapter. Many wrong answers happen because students mix km/h and m/s.

Conversion	Rule
km/h to m/s	Multiply by 5/18
m/s to km/h	Multiply by 18/5
Minutes to hours	Divide by 60
Seconds to hours	Divide by 3600

Example: Convert 72 km/h into m/s.

72 x 5/18 = 20 m/s.

Example: Convert 15 m/s into km/h.

15 x 18/5 = 54 km/h.

Direct Speed, Time and Distance Examples

Example 1

A bus travels 240 km in 4 hours. Find its speed.

Speed = Distance / Time = 240/4 = 60 km/h.

Example 2

A cyclist rides at 18 km/h for 3 hours. Find the distance covered.

Distance = Speed x Time = 18 x 3 = 54 km.

Example 3

A train covers 360 km at 90 km/h. Find the time taken.

Time = Distance / Speed = 360/90 = 4 hours.

Average Speed

Average speed is total distance divided by total time. It is not always the average of speeds. If the time spent at each speed is same, then average of speeds can be used. But if the distances are same, a special formula is used.

Average speed = Total distance / Total time.

If equal distances are covered at speeds x and y, then average speed = 2xy / (x + y).

Example: A person travels from A to B at 40 km/h and returns from B to A at 60 km/h. Find average speed for the whole journey.

Since distances are equal, average speed = 2xy / (x + y).

= 2 x 40 x 60 / (40 + 60) = 4800/100 = 48 km/h.

Average Speed When Time Is Same

If a person travels for equal time at two different speeds, average speed is the simple average of the speeds.

Example: A car travels for 2 hours at 50 km/h and for 2 hours at 70 km/h. Find average speed.

Total distance = 50 x 2 + 70 x 2 = 100 + 140 = 240 km.

Total time = 4 hours.

Average speed = 240/4 = 60 km/h.

This is also equal to (50 + 70)/2 because time is same.

Relative Speed

Relative speed is used when two bodies move at the same time. It helps to find when they meet, cross, or separate.

If two bodies move in opposite directions, relative speed = sum of speeds.

If two bodies move in the same direction, relative speed = difference of speeds.

Example: Two cars start from the same point in opposite directions at 40 km/h and 50 km/h. Find distance between them after 3 hours.

Relative speed = 40 + 50 = 90 km/h.

Distance between them after 3 hours = 90 x 3 = 270 km.

Example: Two runners move in the same direction at 12 km/h and 8 km/h. Find distance between them after 2 hours.

Relative speed = 12 – 8 = 4 km/h.

Distance between them = 4 x 2 = 8 km.

Meeting Point Questions

When two persons start from opposite ends and move towards each other, they meet when together they cover the total distance between the two points.

Formula:

Meeting time = Distance between them / Sum of speeds.

Example: A and B are 300 km apart. They start moving towards each other at 40 km/h and 60 km/h. Find when they meet.

Combined speed = 40 + 60 = 100 km/h.

Time = 300/100 = 3 hours.

Distance covered by A = 40 x 3 = 120 km.

Distance covered by B = 60 x 3 = 180 km.

Chasing Questions

When one moving body follows another in the same direction, use difference of speeds. The faster body gains on the slower body at the relative speed.

Example: A thief is 500 m ahead of a policeman. The thief runs at 8 m/s and the policeman runs at 10 m/s. Find the time taken to catch the thief.

Relative speed = 10 – 8 = 2 m/s.

Time = Distance gap / Relative speed = 500/2 = 250 seconds.

Train Problems

Train problems are part of time and distance because a train has length. When a train crosses a pole, it covers its own length. When a train crosses a platform, it covers its own length plus platform length. When two trains cross each other, they cover the sum of their lengths.

Case	Distance covered
Train crosses pole	Length of train
Train crosses platform	Train length + platform length
Two trains opposite direction	Sum of lengths, speed = sum of speeds
Two trains same direction	Sum of lengths, speed = difference of speeds

Train Example 1

A train 180 m long crosses a pole in 9 seconds. Find its speed in km/h.

Speed = 180/9 = 20 m/s.

20 m/s = 20 x 18/5 = 72 km/h.

Train Example 2

A train 150 m long crosses a platform 250 m long in 20 seconds. Find its speed.

Total distance = 150 + 250 = 400 m.

Speed = 400/20 = 20 m/s = 72 km/h.

Train Example 3

Two trains of lengths 120 m and 180 m move in opposite directions at 36 km/h and 54 km/h. Find crossing time.

Total length = 120 + 180 = 300 m.

Relative speed = 36 + 54 = 90 km/h = 25 m/s.

Time = 300/25 = 12 seconds.

Ratio of Speed and Time

For the same distance, speed and time are inversely proportional. If speed ratio is a:b, then time ratio is b:a.

Example: A and B cover the same distance. A’s speed is 40 km/h and B’s speed is 60 km/h. Find ratio of their times.

Speed ratio = 40:60 = 2:3.

Time ratio = 3:2.

Increasing or Decreasing Speed

If speed increases, time decreases for the same distance. If speed decreases, time increases. Questions may say that a person reaches early or late because of speed change.

Example: A person covers a distance at 40 km/h and reaches 1 hour late. If he travels at 60 km/h, he reaches 1 hour early. Find the distance.

Difference in time between the two speeds = 2 hours.

Let distance be D.

D/40 – D/60 = 2.

(3D – 2D)/120 = 2.

D = 240 km.

Stops and Average Speed

Sometimes a vehicle stops during the journey. Average speed must include the stopped time because total time includes the whole journey duration.

Example: A bus covers 120 km in 3 hours including stoppages. If its running speed is 50 km/h, find stoppage time.

Running time = 120/50 = 2.4 hours.

Total time = 3 hours.

Stoppage time = 3 – 2.4 = 0.6 hour = 36 minutes.

Circular Track Questions

In circular track questions, two people may run in the same direction or opposite directions. If they run in opposite directions, use sum of speeds. If they run in the same direction, use difference of speeds.

Example: A circular track is 400 m long. A and B run in opposite directions at 6 m/s and 4 m/s. When will they meet for the first time?

Relative speed = 6 + 4 = 10 m/s.

Time = 400/10 = 40 seconds.

If they run in the same direction, relative speed = 6 – 4 = 2 m/s, so first meeting time would be 400/2 = 200 seconds.

Common Mistakes

Using km/h directly with metres and seconds.
Taking average speed as simple average when distances are equal.
Forgetting train length while crossing a pole or platform.
Adding speeds when bodies move in same direction.
Subtracting speeds when bodies move in opposite directions.
Ignoring stoppage time in average speed questions.

Solved Examples

Example 1

A car travels 150 km at 50 km/h and 200 km at 100 km/h. Find average speed.

Total distance = 350 km.

Total time = 150/50 + 200/100 = 3 + 2 = 5 hours.

Average speed = 350/5 = 70 km/h.

Example 2

A man walks at 5 km/h. How far will he walk in 2 hours 30 minutes?

2 hours 30 minutes = 2.5 hours.

Distance = 5 x 2.5 = 12.5 km.

Example 3

A train moving at 90 km/h crosses a man walking in the same direction at 6 km/h in 10 seconds. Find train length.

Relative speed = 90 – 6 = 84 km/h = 84 x 5/18 = 70/3 m/s.

Length = speed x time = 70/3 x 10 = 700/3 m = 233.33 m.

Example 4

Two trains cross each other in 15 seconds while moving in opposite directions. Their speeds are 36 km/h and 54 km/h. If one train is 100 m long, find the length of the other train.

Relative speed = 90 km/h = 25 m/s.

Total distance covered = 25 x 15 = 375 m.

Other train length = 375 – 100 = 275 m.

Example 5

A person travels half the distance at 30 km/h and half at 45 km/h. Find average speed.

Average speed = 2xy/(x + y) = 2 x 30 x 45 / 75 = 36 km/h.

Practice Questions

Find speed if distance is 180 km and time is 3 hours.
Convert 54 km/h into m/s.
Convert 25 m/s into km/h.
A train 200 m long crosses a pole in 10 seconds. Find speed in km/h.
Two cars move towards each other from 280 km apart at 60 km/h and 80 km/h. Find meeting time.
A person covers equal distances at 20 km/h and 30 km/h. Find average speed.
A cyclist covers 45 km in 3 hours. Find speed.
A train 100 m long crosses a 300 m platform in 20 seconds. Find speed in m/s.

Answers to Practice Questions

60 km/h.
15 m/s.
90 km/h.
72 km/h.
2 hours.
24 km/h.
15 km/h.
20 m/s.

Frequently Asked Questions

What is the formula of speed?

Speed = Distance / Time.

What is the formula of distance?

Distance = Speed x Time.

What is the formula of time?

Time = Distance / Speed.

How do we convert km/h into m/s?

Multiply the speed by 5/18.

How do we convert m/s into km/h?

Multiply the speed by 18/5.

What is relative speed in opposite direction?

Relative speed is the sum of the two speeds.

What is relative speed in same direction?

Relative speed is the difference between the two speeds.

What distance does a train cover while crossing a platform?

It covers its own length plus the length of the platform.

Revision Notes

For basic questions, use speed = distance/time. For average speed, always use total distance divided by total time. For equal distances at two speeds, use 2xy/(x + y). For relative speed, add speeds in opposite directions and subtract speeds in the same direction.

In train problems, remember to include length. A train crossing a pole covers only its own length, but a train crossing a platform covers train length plus platform length. Careful unit conversion is the key to accurate answers.

Early and Late Arrival Problems

Early and late arrival questions compare two different speeds for the same distance. If a person travels slowly, he reaches late. If he travels faster, he reaches early. The difference between the two times helps us find the distance.

Example: A man travels at 30 km/h and reaches 20 minutes late. If he travels at 40 km/h, he reaches 10 minutes early. Find the distance.

Total difference in time = 20 + 10 = 30 minutes = 1/2 hour.

Let the distance be D km.

D/30 – D/40 = 1/2.

(4D – 3D)/120 = 1/2.

D/120 = 1/2, so D = 60 km.

In these questions, always add the early and late times if one case is late and the other is early.

Same Distance with Changed Speed

If distance is same, time changes inversely with speed. If speed increases by a certain percentage, time decreases, but not by the same percentage. For example, if speed increases by 25 percent, new speed becomes 125 percent of old speed, so time becomes 100/125 = 80 percent of old time. That means time decreases by 20 percent.

Example: A car increases its speed from 40 km/h to 50 km/h. What is the percentage decrease in time for the same distance?

Speed ratio = 40:50 = 4:5.

Time ratio = 5:4.

Decrease in time = 1 part out of 5 parts = 20 percent.

Trains Crossing a Man

When a train crosses a man standing still, distance covered is the length of the train. If the man is moving, use relative speed. A man walking in the same direction reduces relative speed. A man walking in the opposite direction increases relative speed.

Example: A train 240 m long is moving at 72 km/h. It crosses a man walking in the opposite direction at 3 m/s. Find crossing time.

Train speed = 72 x 5/18 = 20 m/s.

Relative speed = 20 + 3 = 23 m/s.

Time = 240/23 = 10.43 seconds approximately.

Two Trains Crossing in Same Direction

When two trains move in the same direction, the faster train must cover the sum of both lengths to completely overtake the slower train. Use the difference of speeds.

Example: A 200 m train moving at 90 km/h overtakes a 150 m train moving at 54 km/h. Find the time taken.

Total distance = 200 + 150 = 350 m.

Relative speed = 90 – 54 = 36 km/h = 10 m/s.

Time = 350/10 = 35 seconds.

Escalator Style Movement Idea

Some advanced questions include moving walkways, escalators, or people walking on a moving path. These are also time and distance questions. If a person moves in the same direction as the moving path, speeds are added. If he moves against it, speeds are subtracted.

Example: A moving walkway moves at 2 km/h. A person walks at 5 km/h on it in the same direction. His effective speed is 7 km/h. If he walks against it, his effective speed is 3 km/h.

This is the same idea as relative speed and boats and streams.

Round Trip Average Speed

Round trip questions are common because the distance going and returning is equal. If speeds are different for onward and return journeys, use the equal-distance formula.

Average speed = 2xy/(x + y).

Example: A person goes to office at 24 km/h and returns at 36 km/h. Find average speed.

Average speed = 2 x 24 x 36 / (24 + 36).

= 1728/60 = 28.8 km/h.

Do not write average speed as 30 km/h, because that would be the simple average and it is not correct for equal distances.

Relative Speed on a Circular Track

On a circular track, two runners meet again and again. The first meeting time depends on relative speed and track length. If they run in opposite directions, they meet quickly. If they run in the same direction, the faster runner must gain one full lap over the slower runner.

Example: A circular track is 600 m. A runs at 8 m/s and B runs at 5 m/s in the same direction. Find when A first meets B again.

Relative speed = 8 – 5 = 3 m/s.

Time = 600/3 = 200 seconds.

If they ran in opposite directions, relative speed would be 8 + 5 = 13 m/s, and first meeting time would be 600/13 seconds.

Using Options in Aptitude Exams

In multiple-choice exams, options can save time. First estimate the answer before doing exact calculation. For example, if a train travels 300 m in about 10 seconds, speed is about 30 m/s or 108 km/h. If all options are far from 108 km/h except one, you can quickly choose the nearest option after checking units.

However, never skip unit conversion. Many options are designed to catch students who forget to convert km/h into m/s or seconds into hours.

Answers to More Practice Questions

72 km/h.
48 km/h.
100 seconds.
60 km.
Total length is 300 m and time is 300/15 = 20 seconds.
250 km.

Conclusion

Time and Distance is a scoring topic when the basic formulas are clear. Keep speed, time, and distance units consistent, use relative speed for moving-body questions, and use total distance by total time for average speed.

Practice different question types such as direct formula questions, unit conversion, trains, meeting points, chasing, circular tracks, and stoppages. These patterns cover most exam-level problems from this chapter.