Question 1
A train runs at a steady 45 km/h for 4 hours.
How far does it travel?
- 11
- 45
- 180
- 49
- 225
Show the worked solution
- Distance = speed × time = 45 × 4 = 180 km.
- Answer: 180 km.
Exam path · Time, Speed & Distance
Time speed and distance questions, one relationship deep
Time speed and distance questions all come from one relationship: distance equals speed multiplied by time. Everything else in the topic is that relationship plus a units conversion or a relative speed. Fix the units first, decide whether the two objects are closing on each other or pulling apart, and the arithmetic that remains is a single multiplication or division.
Speed, distance and the train problems built on them are worth two to three marks in banking prelims and considerably more in railway papers, where the topic is a favourite. It is also where units quietly destroy otherwise correct work: a paper mixes km/h with metres and seconds within the same question, and a candidate who converts at the wrong moment gets a clean wrong answer that is on the option list.
Try it against the clock. Time, Speed & Distance runs at 40s easy, 50s medium and 65s hard. The clock is stamped and judged on our server, so the limit you see is the deadline that is actually enforced — and it starts when you tap Start, not while the question is loading.
How to solve time speed and distance questions without the trap
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Convert the units before anything else
Multiply km/h by 5/18 to get m/s, and m/s by 18/5 to go back. Do it as the first line of working, never in the middle — a conversion applied halfway through is the single largest source of wrong answers in this topic.
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Decide the relative speed by direction
Two objects moving towards each other or in opposite directions: add the speeds. Same direction, one overtaking the other: subtract. Everything about trains crossing, boats and races follows from picking the right one of those two.
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Count the whole distance a train has to cover
A train crossing a pole covers its own length. Crossing a platform or another train, it covers its length plus the other length. Missing the second term is the classic train-question error.
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Use ratios when speed changes and distance does not
For the same distance, time is inversely proportional to speed: raise speed in the ratio 3:4 and time falls in the ratio 4:3. That converts most "if he had walked faster" questions into one proportion instead of two equations.
What distance is actually being covered
| The situation | Distance to use |
|---|---|
| Train crosses a pole or a standing person | Length of the train |
| Train crosses a platform or a bridge | Train length + platform length |
| Two trains cross each other | Sum of both lengths, at the sum or difference of speeds |
| Boat downstream | Speed of boat + speed of stream |
| Boat upstream | Speed of boat − speed of stream |
3 real time speed and distance questions, with worked solutions
Generated by the same engine that mints the ComputePrep daily. Each answer is computed from the numbers printed in the question, and the walkthrough below each one is the engine's own working — not a solution written afterwards. Reload this page's live drill and you get different numbers.
Question 2
A car covers a certain distance at 24 km/h and returns along the same route at 40 km/h.
What is its average speed for the whole journey?
- 33
- 16
- 64
- 32
- 30
Show the worked solution
- Equal distances, different speeds — the average is HARMONIC, not the plain mean.
- Average = 2 × 24 × 40 ÷ (24 + 40) = 1920 ÷ 64 = 30 km/h.
- The tempting 32 km/h is wrong: more time is spent on the slower leg.
- Answer: 30 km/h.
Question 3
A train covers 200 km at a steady 50 km/h.
How long does the journey take?
- 8
- 150
- 1
- 4
- 50
Show the worked solution
- Time = distance ÷ speed = 200 ÷ 50 = 4 hours.
- Answer: 4 hours.
Common mistakes this drill is built from
The wrong options are not random numbers. Each one is the result of a specific careless error for this topic, so picking one tells you which habit is costing you marks.
Mixing km/h with metres and seconds
A question that gives a speed in km/h and a length in metres wants an answer in seconds. Convert at the very start or the error compounds through every later step.
Adding speeds when they should be subtracted
Same direction means the difference, opposite means the sum. Both answers appear in the options because both are the result of a defensible-looking reading of the sentence.
Averaging two speeds
Going somewhere at 40 km/h and back at 60 does not average to 50. Equal distances at different speeds need the harmonic mean, which here is 48 — and 50 is always an option.
Why your answer came out wrong
The specific wrong numbers this topic produces, and what each one tells you about the step you took. If you have just got a question wrong and want to know which habit did it, start here.
A train at 72 km/h crosses a 200 m platform — why is my answer out by a factor of 3.6?
Because km/h met metres. Convert first: 72 × 5/18 = 20 m/s. The distance is the train's length plus the platform's length, in metres, divided by the speed in metres per second. Leaving anything in km/h puts the answer out by exactly 3.6 every time.
Two trains — do I add the speeds or subtract them?
Opposite directions add: 60 and 40 give a relative speed of 100 km/h. Same direction subtracts: 60 and 40 give 20. The check is the time. Overtaking always takes far longer than crossing, so if your overtaking answer is the smaller of the two, you added where you should have subtracted.
I drove out at 40 km/h and back at 60 — why is the average speed not 50?
Because the distances are equal, not the times, and you spend longer at the slower speed. Use the harmonic mean: 2 × 40 × 60 ÷ (40 + 60) = 48 km/h. The average of two speeds is only their plain average when the two are travelled for equal times, which almost never happens in these questions.
FAQ
How do I convert km/h to m/s quickly?
Multiply by 5/18. To go the other way, from m/s to km/h, multiply by 18/5. Doing this conversion as the first step of the working, rather than partway through, prevents most of the errors in this topic.
When do I add speeds and when do I subtract them?
Add when the objects move towards each other or in opposite directions, subtract when they move in the same direction and one is overtaking. For boats, downstream adds the stream speed and upstream subtracts it.
What distance does a train cover when crossing a platform?
Its own length plus the length of the platform. Crossing a pole or a stationary person, it covers only its own length. Forgetting the second term is the most common train-question mistake.
How long should these questions take?
Between 40 and 65 seconds in prelims. The drill enforces 40 seconds on easy, 50 on medium and 65 on hard, stamped and judged on the server rather than in your browser.
Are railway exam maths questions the same as bank ones?
The topic overlaps heavily, and RRB papers lean on speed, distance and time more than banking papers do. The arithmetic and the methods are identical, so this drill serves both.
Practise the next topic
- All 23 drill types — the full rotation with every published time limit.
- Time and work questions — time and work questions, timed.
- Average questions — average questions, timed.
- Vedic maths shortcuts — the seven sutras that make a 15-second answer possible.
- How to improve calculation speed — the six-week arc these drills fit into.
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