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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 a regular GRE Quant and GMAT problem-solving topic. It is also where units quietly destroy otherwise correct work: a question mixes miles per hour with feet and seconds, 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 90s easy, 105s medium and 120s 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.

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How to solve time speed and distance questions without the trap

  1. Convert the units before anything else

    60 miles per hour is 88 feet per second, so multiply miles per hour by 22/15 to get feet per second, and feet per second by 15/22 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.

  2. 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.

  3. 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.

  4. 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 situationDistance to use
Train crosses a pole or a standing personLength of the train
Train crosses a platform or a bridgeTrain length + platform length
Two trains cross each otherSum of both lengths, at the sum or difference of speeds
Boat downstreamSpeed of boat + speed of stream
Boat upstreamSpeed of boat − speed of stream

3 sample time speed and distance questions, with worked solutions

Generated by the same engine that mints the Quant Daily 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 1

A car travels at a constant 45 miles per hour for 4 hours.

What distance does it cover?

  1. 225
  2. 192
  3. 180
  4. 135
  5. 150
Show the worked solution
  1. Distance = speed × time = 45 × 4 = 180 miles.
  2. Answer: 180 miles.

Question 2

A car travels a certain distance at 10 miles per hour and returns along the same route at 40 miles per hour.

What is the average speed for the entire trip?

  1. 16
  2. 50
  3. 56
  4. 14
  5. 25
Show the worked solution
  1. Equal distances, different speeds — the average is HARMONIC, not the plain mean.
  2. Average = 2 × 10 × 40 ÷ (10 + 40) = 800 ÷ 50 = 16 miles per hour.
  3. The tempting 25 miles per hour is wrong: more time is spent on the slower leg.
  4. Answer: 16 miles per hour.

Question 3

A car travels a certain distance at 12 miles per hour and returns along the same route at 36 miles per hour.

What is the average speed for the entire trip?

  1. 24
  2. 48
  3. 33
  4. 25
  5. 18
Show the worked solution
  1. Equal distances, different speeds — the average is HARMONIC, not the plain mean.
  2. Average = 2 × 12 × 36 ÷ (12 + 36) = 864 ÷ 48 = 18 miles per hour.
  3. The tempting 24 miles per hour is wrong: more time is spent on the slower leg.
  4. Answer: 18 miles per hour.

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 miles per hour with feet and seconds

A question that gives a speed in miles per hour and a length in feet 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 miles per hour 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 30 miles per hour crosses a 440-foot platform — why is my answer so far out?

Because miles per hour met feet. Convert first: 30 × 22/15 = 44 feet per second. The distance is the train's length plus the platform's length, in feet, divided by the speed in feet per second. Dividing feet by miles per hour gives a number in no unit at all, and that number is printed as an option.

Two trains — do I add the speeds or subtract them?

Opposite directions add: 60 and 40 give a relative speed of 100 miles per hour. 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 miles per hour 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 miles per hour. 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 miles per hour to feet per second quickly?

Multiply by 22/15 — 60 miles per hour is exactly 88 feet per second. To go the other way, multiply by 15/22. 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 90 and 120 seconds in the timed section. The drill enforces 90 seconds on easy, 105 on medium and 120 on hard, stamped and judged on the server rather than in your browser.

Are train problems the same as other speed questions?

They use the same distance = speed × time relationship, plus a length. A train crossing a platform covers its own length plus the platform. The arithmetic is identical to any other relative-speed question once the distance is right.

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