Speed, Distance & Time

Find any one of speed, distance or time with every unit conversion shown — plus average speed for a journey in parts, relative speed, and the full set of train-and-platform problems, each animated on a line.

Class 5–10 Mathematics km/h ↔ m/s Train problems

Speed = Distance ÷ Time, Distance = Speed × Time and Time = Distance ÷ Speed. A journey of 150 km in 2.5 hours gives 150 ÷ 2.5 = 60 km/h. To change km/h into m/s multiply by 5/18, so 72 km/h = 20 m/s; multiply by 18/5 to go the other way. The units of distance and time must match the speed.

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Answer

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Step-by-step working

    How it works

    One triangle solves every question

    Speed, distance and time are locked together by a single relationship. Cover the one you need and the formula appears — this tool does exactly that, and shows every unit change on the way.

    Pick what to find

    Speed, distance or time — then type the other two with their units.

    Units handled for you

    Mix km with minutes if you like; the steps show every conversion in full.

    Watch the journey

    The animation moves along a line so the answer feels real, not just a number.

    Harder questions

    Average speed, relative speed and the whole train-and-platform set, with formulas.

    The three formulas

    Speed = Distance ÷ Time

    Distance = Speed × Time   Time = Distance ÷ Speed

    Distance and time must be in units that match the speed — that is where most marks are lost.

    km/h ↔ m/s

    1 km = 1000 m and 1 hour = 3600 s, so 1 km/h = 1000 ÷ 3600 m/s = 5/18 m/s.

    km/h → m/s : × 5/18   m/s → km/h : × 18/5

    Worth memorising: 18 km/h = 5 m/s, 36 = 10, 54 = 15, 72 km/h = 20 m/s, 90 = 25, 108 = 30.

    Average speed

    Average speed = Total distance ÷ Total time

    Never add the speeds and halve them. For equal distances at u and v the answer is the harmonic mean 2uv ÷ (u + v) — 40 and 60 km/h gives 48 km/h, not 50.

    Train problems

    A train crossing something must cover its own length plus that object's length.

    Pole: t = L ÷ v. Platform: t = (L + P) ÷ v. Two trains: t = (L₁ + L₂) ÷ (v₁ + v₂) if they are moving in opposite directions, or ÷ (v₁ − v₂) in the same direction.

    Exam check: a 150 m train at 90 km/h (= 25 m/s) crossing a 250 m platform must cover 150 + 250 = 400 m, so it takes 400 ÷ 25 = 16 seconds. If you forget the train's own length you get 10 seconds — the commonest mistake in the chapter.
    Questions & answers

    Speed, Distance & Time — your questions

    What is the formula for speed, distance and time?

    Speed = Distance ÷ Time, Distance = Speed × Time and Time = Distance ÷ Speed. Cover the quantity you want in the triangle and the formula is what remains. The distance and time units must match the speed unit — using kilometres with minutes against an answer in km/h is where most marks are lost.

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

    Multiply by 5/18, because 1 km = 1000 m and 1 hour = 3600 s, so 1 km/h = 1000 ÷ 3600 = 5/18 m/s. For example 72 km/h × 5/18 = 20 m/s. To go from m/s back to km/h, multiply by 18/5. Worth memorising: 18 km/h = 5 m/s, 36 = 10, 54 = 15, 72 = 20 and 90 = 25.

    How do I find the average speed of a journey?

    Average speed = total distance ÷ total time. Never add the two speeds and halve them. For equal distances covered at u and v, the average is the harmonic mean 2uv ÷ (u + v), so travelling at 40 km/h and 60 km/h over equal distances gives 48 km/h, not 50 km/h.

    How long does a train take to cross a platform?

    The train must cover its own length plus the length of the platform, so t = (L + P) ÷ v. A 150 m train at 90 km/h, which is 25 m/s, crossing a 250 m platform covers 150 + 250 = 400 m and takes 400 ÷ 25 = 16 seconds. Forgetting the train's own length gives 10 seconds, the commonest error in this chapter.

    What is relative speed?

    Relative speed is how fast the gap between two moving objects closes or opens. Moving towards each other, add the speeds; moving in the same direction, subtract them. Two trains at 60 km/h and 40 km/h approaching across a 250 km gap close it at 100 km/h, meeting after 250 ÷ 100 = 2.5 hours.

    How long does a train take to pass a pole?

    A pole or a standing person has no length, so the train only needs to cover its own length: t = L ÷ v. A 150 m train at 90 km/h, which is 25 m/s, passes a pole in 150 ÷ 25 = 6 seconds. When two trains pass each other, add their lengths and add their speeds if they are moving in opposite directions.