Speed, Distance and Time Notes for SSC Exams

Speed, Distance and Time is a core chapter of SSC Quantitative Aptitude. Two or three questions come from it in each Tier 1 paper, and trains, boats and streams and races use the same relations. These speed, distance and time notes for SSC explain the formulas, unit conversions and relative speed with solved examples and practice questions.

Basic Relation

Speed tells how fast an object moves. The three quantities are connected by one simple formula.

• Speed = Distance / Time
• Distance = Speed x Time
• Time = Distance / Speed
• When the distance is the same, speed and time are inversely proportional.
• When the time is the same, distance is directly proportional to speed.

Unit Conversion

For example, 72 km/h = 72 x 5/18 = 20 m/s, and 25 m/s = 25 x 18/5 = 90 km/h. Memorise the common pairs: 18 km/h = 5 m/s, 36 km/h = 10 m/s, 54 km/h = 15 m/s, 72 km/h = 20 m/s and 90 km/h = 25 m/s.

Average Speed

• Average speed = Total distance / Total time.
• For equal distances at speeds x and y: 2xy / (x + y).
• For equal times at speeds x and y: (x + y) / 2.
• Never take the simple average of two speeds when the distance is the same.

Relative Speed

Late and Early Arrival

In these problems, the distance is the same and the time changes with the speed. Write the difference of the two times equal to the total time difference. If a person walking at 5 km/h reaches 10 minutes late and at 6 km/h reaches 10 minutes early, then d/5 - d/6 = 20/60, which gives d = 10 km.

Solved Examples

Example 1: Convert 72 km/h into m/s.
Solution: 72 x 5/18 = 20 m/s.

Example 2: A car covers 150 km in 3 hours. Find its speed.
Solution: Speed = 150 / 3 = 50 km/h.

Example 3: A man walking at 5 km/h reaches his office 10 minutes late. When he walks at 6 km/h, he reaches 10 minutes early. Find the distance.
Solution: d/5 - d/6 = 20/60, so d/30 = 1/3 and d = 10 km.

Example 4: Two trains start from two stations 300 km apart and move towards each other at 60 km/h and 40 km/h. When will they meet?
Solution: Relative speed = 60 + 40 = 100 km/h. Time = 300 / 100 = 3 hours.

Example 5: A starts 2 hours earlier at 6 km/h. B follows at 8 km/h. When will B catch A?
Solution: Gap after 2 hours = 12 km. Relative speed = 8 - 6 = 2 km/h. Time = 12 / 2 = 6 hours after B starts.

Example 6: The ratio of the speeds of two cars is 3 : 4. The slower car takes 2 hours more to cover the same distance. Find the time of each.
Solution: Time ratio = 4 : 3. One part = 2 hours, so slower = 8 hours and faster = 6 hours.

Quick Tips to Solve Faster

• Convert all the speeds into the same unit before solving.
• For equal distances, use 2xy/(x + y) for the average speed.
• In "late and early" questions, write one equation of the time difference.
• For the same distance, speed ratio is the inverse of the time ratio.
• Draw a quick line diagram for meeting and catching-up problems.

Common Mistakes to Avoid

• Taking the simple average of two speeds for a return journey.
• Adding speeds when the objects move in the same direction.
• Mixing km/h and m/s in one equation.
• Using minutes directly in the formula instead of converting into hours.
• Forgetting the head start gap in catch-up problems.

Quick Revision Points

• Speed = Distance / Time.
• km/h to m/s: multiply by 5/18.
• Opposite direction: add speeds. Same direction: subtract speeds.
• Average speed for equal distances = 2xy / (x + y).
• Same distance: speed is inversely proportional to time.

Practice Questions With Answers

1. Convert 54 km/h into m/s.
   Answer: 15 m/s (54 x 5/18).
2. Convert 25 m/s into km/h.
   Answer: 90 km/h (25 x 18/5).
3. A car travels 240 km at 60 km/h. How long does it take?
   Answer: 4 hours (240 / 60).
4. A man goes up at 20 km/h and comes down at 30 km/h. Find the average speed.
   Answer: 24 km/h (2 x 20 x 30 / 50).
5. Walking at 3/4 of his usual speed, a man is 20 minutes late. Find his usual time.
   Answer: 60 minutes (Time becomes 4/3, extra = 1/3 of usual).
6. Two persons start from points 12 km apart and walk in the same direction at 7 km/h and 5 km/h. When will the faster catch the slower, if the faster is behind?
   Answer: 6 hours (12 / 2).
7. Find the distance covered at 8 km/h in 2.5 hours.
   Answer: 20 km (8 x 2.5).
8. Two cars start from the same point in opposite directions at 40 km/h and 60 km/h. How far apart are they after 3 hours?
   Answer: 300 km (100 x 3).
9. A man covers a distance in 12 hours. How long will he take if his speed is increased by 20%?
   Answer: 10 hours (12 / 1.2).
10. How long does a car at 36 km/h take to cover 600 m?
    Answer: 60 seconds (36 km/h = 10 m/s).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching SSC problems on trains practice paper to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Average Notes
• Time and Work Notes
• Ratio and Proportion Notes
• Percentage Notes
• SSC Problems on Trains Practice Paper
• SSC Boats and Streams Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What is the formula for speed, distance and time?

Speed = Distance / Time, Distance = Speed x Time and Time = Distance / Speed.

How many questions come from this chapter in SSC exams?

Two or three questions come directly, and trains, boats and streams and races add more.

How do I convert km/h to m/s?

Multiply the speed in km/h by 5/18 to get m/s.

What is the average speed formula for equal distances?

Average speed = 2xy / (x + y), where x and y are the two speeds.

What is relative speed?

Relative speed is the speed of one object as seen from another. It is the sum of the speeds for opposite directions and the difference for the same direction.

Why is the simple average of speeds wrong?

Because more time is spent at the lower speed, the average speed is always closer to the lower speed. The correct formula uses total distance divided by total time.

What is the relation between speed and time for a fixed distance?

They are inversely proportional. If the speed doubles, the time halves.

Which chapters use the same formulas?

Problems on trains, boats and streams, races and circular tracks and time and work (in a similar form) use speed-distance-time ideas.

How should I practise this chapter?

Learn the conversions, solve the examples and practice questions and then attempt train and boat practice papers.