Time, Speed and Distance Formula Guide for SSC Exams
Rahul Kumar
SSC Exam Expert & Content Editor
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Time, speed and distance is one of the most repeated topics in SSC Quantitative Aptitude, and the trains, boats and races questions come from the same three formulas. This time, speed and distance formula guide for SSC gives the basic formula, the unit conversions, the average and relative speed formulas, and the special formulas for trains, boats and streams, and races, with solved examples.
Basic Formulas
| Item | Formula |
|---|---|
| Speed | Distance / Time |
| Distance | Speed × Time |
| Time | Distance / Speed |
| km/h to m/s | Multiply by 5/18 |
| m/s to km/h | Multiply by 18/5 |
| For the same distance | Speed and time are inversely proportional, so the ratio of the times is the reverse of the ratio of the speeds |
| For the same time | Distance is directly proportional to speed |
| If the speed becomes a/b of the old speed | The time becomes b/a of the old time |
Speed Conversion Table
| km/h | m/s |
|---|---|
| 18 | 5 |
| 36 | 10 |
| 54 | 15 |
| 72 | 20 |
| 90 | 25 |
| 108 | 30 |
Average Speed
| Case | Formula |
|---|---|
| Total distance and total time are known | Average speed = Total distance / Total time |
| Equal distances at speeds x and y | 2xy / (x + y) |
| Equal times at speeds x and y | (x + y) / 2 |
Relative Speed
| Case | Relative speed |
|---|---|
| Two objects move in opposite directions (towards or away from each other) | Sum of the speeds (x + y) |
| Two objects move in the same direction | Difference of the speeds (x − y) |
The time of meeting of two persons who start from two points at the distance D and walk towards each other is D / (x + y).
Trains
| Case | Formula for the time taken |
|---|---|
| A train crosses a pole or a standing person | Length of the train / Speed of the train |
| A train crosses a platform or a bridge | (Length of the train + Length of the platform) / Speed of the train |
| Two trains cross each other in opposite directions | (L1 + L2) / (S1 + S2) |
| Two trains cross each other in the same direction | (L1 + L2) / (S1 − S2) |
| A train crosses a man who is walking | Length of the train / Relative speed |
Boats and Streams
| Item | Formula |
|---|---|
| Downstream speed (D) | u + v, where u is the speed of the boat in still water and v is the speed of the stream |
| Upstream speed (U) | u − v |
| Speed of the boat in still water | (D + U) / 2 |
| Speed of the stream | (D − U) / 2 |
| Average speed for a round trip | Total distance / Total time, or (D × U) / u |
Races
- If A beats B by x metres in a race of d metres, then when A has run d metres, B has run (d − x) metres.
- If A gives B a start of x metres, then A has to run d metres while B runs (d − x) metres.
- If A beats B by t seconds, then B needs t more seconds to finish the race.
- In a dead heat, both runners reach the finish at the same time.
Circular Track
- If two persons run in opposite directions on a circular track, they meet after (circumference) / (x + y).
- If they run in the same direction, the faster runner meets the slower one after (circumference) / (x − y).
Solved Examples
Example 1. A train 150 m long crosses a platform 250 m long at 72 km/h. How long does it take?
72 km/h = 20 m/s. Time = (150 + 250) / 20 = 20 seconds.
Example 2. Two trains of length 125 m and 175 m run in opposite directions at 50 km/h and 40 km/h. In how much time do they cross each other?
The relative speed = 90 km/h = 25 m/s. Time = (125 + 175) / 25 = 12 seconds.
Example 3. A boat goes downstream at 15 km/h and upstream at 9 km/h. Find the speed of the boat in still water and the speed of the stream.
Boat = (15 + 9)/2 = 12 km/h. Stream = (15 − 9)/2 = 3 km/h.
Example 4. A person goes from A to B at 30 km/h and returns at 20 km/h. Find the average speed.
2 × 30 × 20 / (30 + 20) = 1200 / 50 = 24 km/h.
Example 5. A and B run a 100 m race. A finishes in 20 seconds and B in 25 seconds. By how many metres does A win?
In 20 seconds, B runs (100/25) × 20 = 80 m. So A wins by 20 metres.
Quick Tips
- Convert all the units into km/h or into m/s before you use a formula.
- For trains, add the lengths when two trains cross, or when a train crosses a platform.
- Use the average speed formula 2xy/(x + y) only when the distances are equal.
- Draw a small diagram for the races and the meeting problems.
Quick Revision Points
- km/h to m/s: multiply by 5/18.
- Average speed for equal distances = 2xy/(x + y).
- Relative speed: add for opposite directions, subtract for the same direction.
- Boat in still water = (D + U)/2 and stream = (D − U)/2.
- A train crossing a platform covers its length plus the length of the platform.
Practice Questions With Answers
- Convert 90 km/h into m/s.
Answer: 25 m/s - Convert 20 m/s into km/h.
Answer: 72 km/h - A 200 m train runs at 36 km/h. Find the time it takes to cross a pole.
Answer: 20 seconds - A 300 m train runs at 54 km/h. Find the time it takes to cross a 300 m platform.
Answer: 40 seconds - The speed of a boat in still water is 8 km/h and the speed of the stream is 2 km/h. Find the upstream speed.
Answer: 6 km/h - The downstream speed is 20 km/h and the upstream speed is 10 km/h. Find the speed of the stream.
Answer: 5 km/h - Find the average speed for equal distances at 60 km/h and 40 km/h.
Answer: 48 km/h - Two trains of length 150 m and 100 m run in opposite directions at 36 km/h and 54 km/h. Find the time to cross.
Answer: 10 seconds - A car covers 120 km in 3 hours. Find the time for 200 km at the same speed.
Answer: 5 hours - If the speed is increased by 25%, by how much % does the time taken change?
Answer: The time decreases by 20%
How to Practise This Chapter
Write each formula on a card, with a solved example on the back, and revise the cards every day. Then test yourself with our practice papers and the previous year papers page. See all guides on the Formula Guide page, and also read the Mathematics notes and Quantitative Aptitude notes. The previous guide is Ratio, Proportion, Mixture and Partnership and the next guide is Time and Work, Pipes and Cisterns.
Frequently Asked Questions
What is the formula for speed?
Speed is the distance divided by the time.
How do I convert km/h into m/s?
Multiply the speed in km/h by 5/18.
How do I convert m/s into km/h?
Multiply the speed in m/s by 18/5.
What is the average speed for equal distances?
It is 2xy divided by (x + y), where x and y are the two speeds.
What is the relative speed for opposite directions?
It is the sum of the two speeds.
What is the relative speed for the same direction?
It is the difference of the two speeds.
How long does a train take to cross a platform?
It takes (length of the train + length of the platform) divided by the speed of the train.
What are downstream and upstream speeds?
Downstream speed is boat speed plus stream speed, and upstream speed is boat speed minus stream speed.
How do I find the speed of the boat in still water?
Take half of the sum of the downstream and upstream speeds.
What happens to the time when the speed increases?
For the same distance the time decreases in the reverse ratio of the speed.
Is this topic asked in SSC exams?
Yes. Time, speed and distance questions are asked in every SSC maths paper.
How many questions come from this topic in SSC exams?
Usually two to four questions, but the number changes from exam to exam.
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Ratio, Proportion, Mixture and Partnership Formula Guide for SSC Exams
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Time and Work, Pipes and Cisterns Formula Guide for SSC Exams
Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.