Relative Speed Trains Questions

📑 On this page

⚡ The short answer

Relative speed is how fast the gap between two moving things changes. Same direction: subtract speeds. Opposite: add them. A crossing train covers its own length plus whatever it crosses. Convert km/h to m/s (× 5/18) first. The trap: platforms and trains have length too.

🎬 The 30-second story

The express that crawled, then flashed

“Why is this express overtaking us in slow motion?”

🚆

Aarav

Their local: 54 km/h. The express: 72.

“From our window it's doing 18 km/h. Five metres a second.”

🪟

Zoya

Local: 170 m long. Express: 180 m.

“Seventy seconds! Yesterday it flashed past in ten.”

⏱️

Aarav

Yesterday it came the other way.

“Yesterday it was coming at us. 72 + 54 = 126 km/h.”

↔️

Zoya

Same trains, same lengths.

Tara's maths: To pass completely, the trains clear 170 + 180 = 350 m. Same way: 18 km/h = 5 m/s, so 70 s. Opposite: 126 km/h = 35 m/s, so 10 s. Only the relative speed changed.

What is relative speed, and when do you add or subtract?

Relative speed is the speed one object seems to have when you watch it from the other: how fast the gap between them changes. Two cars heading north at 80 and 60 km/h: each hour the faster gains 80 − 60 = 20 km. Turn one round to face the other and the gap shrinks by 80 + 60 = 140 km an hour. That's the whole rule.

⚔️ Side by side

Same direction vs opposite directions

➡️➡️Same direction

one chases the other

•S₁ − S₂

➡️⬅️Opposite directions

towards or away from each other

•S₁ + S₂

Test	Same direction	Opposite directions
72 and 54 km/h	18 km/h	126 km/h
Gap changes each hour by	the difference	the sum

Bigger relative speed, shorter crossing: 70 s vs 10 s.

📌 Freeze one train, move the other

Pretend your train is standing still. The other now moves past you at the relative speed, and the problem shrinks to one moving object. Every question here is that trick.

How do you solve train crossing questions?

A train is not a dot. It has crossed a pole only when its last coach passes it, so the front has travelled the train's full length. It has crossed a platform when the last coach leaves the far end: train plus platform. Get the distance right and the rest is one division.

🧮 The formula

What a train must cover to 'cross' something

🚆

Train's length

always

🛤️

Length it crosses

0 for a pole

📏

Distance to clear

÷ relative speed = time

The train crosses…	Distance to cover	Speed to use
A pole, signal or standing person	Train's length	Train's speed
A platform, bridge or tunnel	Train + platform	Train's speed
A person walking or cycling	Train's length	Difference (same way) or sum (towards)
Another train	Both lengths added	Difference (same way) or sum (opposite)

→ scroll to see more

✍️ Worked example Warm-up ⏱ 30 sec

Pole first, then platform

A 210 m metro train passes a signal pole in 14 seconds. At the same speed, how long will it take to cross a 330 m platform?

1
Pole: the train covers its own 210 m. Speed = 210 ÷ 14 = 15 m/s.
2
Platform: distance = 210 + 330 = 540 m.
3
Time = 540 ÷ 15 = 36 s.

Answer: 36 seconds

⚡ Ratio route

Same speed, so time grows with distance: 14 × 540/210 = 36 s.

✍️ Worked example CLAT level ⏱ 45 sec

Overtaking a cyclist

A 280 m train overtakes Rohan, who is cycling at 18 km/h in the same direction, in 16 seconds. Find the train's speed in km/h.

1
Rohan has no real length, so the distance is the train's 280 m.
2
Relative speed = 280 ÷ 16 = 17.5 m/s = 63 km/h.
3
Same direction: relative = train − Rohan, so train = 63 + 18 = 81 km/h.

Answer: 81 km/h (63 is the trap: that's the relative speed)

⚡ The exam-hall shortcut

18 km/h = 5 m/s. Train = 17.5 + 5 = 22.5 m/s = 22.5 × 3.6 = 81 km/h.

✍️ Worked example Tricky ⏱ 75 sec

Find the length, then meet a second train

A train passes a pole in 10 s and a 200 m platform in 18 s. How long will it take to cross a 150 m train coming the other way at 54 km/h?

1
The extra 8 s covered the 200 m platform: speed = 25 m/s.
2
Length = 25 × 10 = 250 m.
3
Other train: 54 km/h = 15 m/s. Opposite, so relative = 25 + 15 = 40 m/s.
4
Time = (250 + 150) ÷ 40 = 10 s.

Answer: 10 seconds

⚡ The exam-hall shortcut

The pole-vs-platform gap gives the speed in one step.

💡 Speeds that are multiples of 18 convert cleanly

18 km/h = 5 m/s, so 36 → 10, 54 → 15, 72 → 20, 90 → 25. Setters pick these on purpose. km/h → m/s must make the number smaller.

🎛️ Try it yourself — change any number

Replay the express and the local

Both lengths added (m) Express (km/h) Local (km/h)

Same direction: relative speed

18 km/h → 70 s

Opposite directions: relative speed

126 km/h → 10 s

Time = total length ÷ relative speed (in m/s, so × 5/18)

As set: 70 s overtaking, 10 s head-on. Push the express to 90 km/h and overtaking drops to 35 s: double the relative speed, half the time.

How do meeting and catch-up problems work?

Same rule, minus the lengths. Heading towards each other, the gap closes at the sum of speeds; in a chase, at the difference. Time = gap ÷ relative speed. The only extra job is finding the gap at the moment both are moving.

🕒 Timeline

Zoya chases Aarav to the fest venue

🛵
9:00

Aarav leaves at 40 km/h
🏍️
9:30

Zoya leaves at 60 km/h

Aarav already has 40 × ½ = 20 km head start.
➖
Gap

Closing speed = 60 − 40 = 20 km/h

20 km ÷ 20 km/h = 1 hour.
🤝
10:30

Caught, 60 km from home

Check: 60 × 1 = 40 × 1.5 = 60 km. ✓

Now flip it. Two buses leave towns 180 km apart together, driving towards each other at 50 and 40 km/h. The gap shrinks at 90 km/h, so they meet after 2 hours, 100 km from the first town: distances split in the ratio of speeds, 50 : 40.

How do race questions like "A beats B by 20 m" work?

Runners start together and run for the same time, so distances covered are in the ratio of their speeds. "A beats B by 20 m in a 100 m race" means that when A touches 100 m, B is at 80 m. B's speed is 80/100 of A's, all race long.

The race says…	What it means	In a 100 m race
A beats B by 20 m	B is 20 m short at A's finish	B runs 80 while A runs 100
A beats B by 5 s	B finishes 5 s after A	B's time = A's time + 5
A beats B by 20 m or 5 s	B needs 5 s for the last 20 m	B's speed = 4 m/s
A gives B a 10 m start	B begins 10 m ahead	B runs only 90 m

→ scroll to see more

✍️ Worked example Tricky ⏱ 50 sec

Chaining two leads

In a 1 km race, Zoya beats Aarav by 50 m, and Aarav beats Meher by 100 m. By how much does Zoya beat Meher?

1
When Zoya finishes, Aarav is at 950 m.
2
Meher runs 900 m per 1,000 of Aarav's, so 0.9 of whatever Aarav runs.
3
At Aarav's 950, Meher is at 950 × 0.9 = 855 m. Gap = 145 m.

Answer: 145 m, not 150 m

⚡ The exam-hall shortcut

Multiply the fractions finished: 0.95 × 0.90 = 0.855. It's combining ratios A:B and B:C.

How do trains hide inside a CLAT caselet?

Since 2020, trains arrive as a paragraph, not a one-liner. Pull the numbers into a table first. Say Rampur Junction's 300 m platform sees Train P (300 m, 90 km/h), Train Q (200 m, 72 km/h) and Train R (450 m, 54 km/h); P and Q run east, R west.

📊 The data

Seconds each train takes to clear Rampur's 300 m platform

Train P (300 m, 90 km/h) · 600 m ÷ 25 m/s

24 s

Train Q (200 m, 72 km/h) · 500 m ÷ 20 m/s

25 s

Train R (450 m, 54 km/h) · 750 m ÷ 15 m/s

50 s

P is longer than Q yet quicker. Compute; don't eyeball.

Then the questions pair trains. P overtaking Q: (300 + 200) ÷ (25 − 20) = 100 s. P crossing R head-on: (300 + 450) ÷ (25 + 15) = 18.75 s.

⚠️ The "cannot be determined" trap

If a passage gives two trains' speeds but not whether they run the same way or opposite, the crossing time could be 100 s or 11.1 s: it cannot be found. Same if a length is missing.

Which traps cost the most marks?

🧭 Decision flow

Before you divide: four checks

❓ Do the units match?

No →

Convert first: km/h × 5/18 = m/s.

Yes ↓

❓ Does the thing being crossed have length (platform, bridge, tunnel, train)?

No →

Distance = the train's length only.

Yes ↓

❓ Is the other thing moving?

No →

Both lengths ÷ the train's speed.

Yes ↓

❓ Is the direction given?

Yes →

Both lengths ÷ (difference if same way, sum if opposite).

No →

Cannot be determined.

Boats and streams: the same idea with water

Boat speed b, river speed s. Downstream: b + s. Upstream: b − s. So s is half the difference of the two.

How CLAT asked it

📝 Asked in CLAT 2019 · Q45 Train through a tunnel

A train 600 meters long is running at a speed of 90 kms/hr. If it crosses a tunnel in one minute, then the length of the tunnel is:

A500 meters

B550 meters

C600 meters

D900 meters

Reveal answer + reasoning

Answer: D

No official key for 2019; this is our solution. Speed = 90 × 5/18 = 25 m/s. In 60 s the train covers 1,500 m = train + tunnel. Tunnel = 1,500 − 600 = 900 m. About 30 seconds.

Why the others fail

A — No correct route gives 500; a guess near the train's length.
B — Also no route. Convert, multiply, subtract the train: 900.
C — Assumes the tunnel equals the train. The 1,500 m total leaves 900 for the tunnel.

📝 Asked in CLAT 2019 · Q47 Chaining race leads

In a 100 meters race, A beats B by 20 meters B beats C by 5 meters. In the same race, A beats C by:

A26 meters

B25 meters

C24 meters

D22 meters

Reveal answer + reasoning

Answer: C

No official key for 2019; this is our solution. When A finishes, B is at 80 m. C runs 95 m per 100 m of B's, so C is at 80 × 0.95 = 76 m. A beats C by 24 m.
Faster: 0.8 × 0.95 = 0.76. About 25 seconds.

Why the others fail

A — No ratio route gives 26.
B — Adds 20 + 5. B's 5 m lead is over 100 m; when A finishes, B has run only 80, so C trails B by 4.
D — No ratio route gives 22.

💥 Myth vs fact

Myth vs fact

🙅 Myth

The relative speed of two trains is the sum of their speeds.

Tap to bust it →

✅ Fact

Only when they move towards or away from each other. Same way: the difference.

🙅 Myth

Crossing a 300 m platform means covering 300 m.

Tap to bust it →

✅ Fact

It covers its own length plus 300 m.

🙅 Myth

If A beats B by 20 m and B beats C by 5 m, A beats C by 25 m.

Tap to bust it →

✅ Fact

It is 24 m: when A finishes, B has run only 80.

🙅 Myth

A train passes a walker in the same time whichever way he walks.

Tap to bust it →

✅ Fact

Walking towards it adds his speed; walking away subtracts it.

Can you do these five?

🎯 Quick quiz

Five relative speed checks

0 / 5

A 360 m goods train at 54 km/h crosses a 240 m bridge.

Q1. How long does it take?

Trains of 120 m and 180 m run in opposite directions at 50 and 40 km/h.

Q2. How long do they take to cross each other?

Kabir's delivery rider leaves at 30 km/h. Twenty minutes later Kabir follows on the same road at 45 km/h.

Q3. How long after setting off does Kabir catch him?

In a 200 m race, Meher beats Rohan by 25 m or 5 seconds.

Q4. What is Meher's time for the race?

A boat goes 24 km downstream in 2 hours and back upstream in 3 hours.

Q5. What is the speed of the stream?

🎯 Relative speed in a nutshell

Relative speed = how fast the gap changes: difference for the same direction, sum for opposite.
A crossing train covers its length + the other object's.
Catch-up = head start ÷ difference; meeting = gap ÷ sum.
In races, multiply leads as ratios; never add them.
No direction or a missing length in a caselet = cannot be determined.

📎 Formula card

Relative speed: same direction S₁ − S₂; opposite S₁ + S₂
Units: km/h × 5/18 = m/s; m/s × 18/5 = km/h
Train: pole T = L ÷ S; platform (L + P) ÷ S; two trains (L₁ + L₂) ÷ (S₁ ± S₂)
Catch-up: head start ÷ (S₁ − S₂). Meeting: gap ÷ (S₁ + S₂)
Race: beats by x m in D m → B : A = (D − x) : D; by x m or t s → B's speed = x ÷ t
Boats: down b + s, up b − s
Circular track C: first meeting C ÷ (S₁ ± S₂)

Frequently asked questions

What is relative speed?

Relative speed is the speed of one moving object as seen from another: how fast the gap between them changes. Same direction, subtract the speeds; towards or away from each other, add them. Trains at 72 and 54 km/h close at 18 km/h one way, 126 km/h head-on.

How do you calculate the time a train takes to cross a platform?

Add the train's length to the platform's, because the train has crossed only when its last coach leaves. Divide by the speed in metres per second. A 210 m train at 15 m/s crossing a 330 m platform covers 540 m, taking 36 seconds.

How do you solve 'A beats B by x metres' race questions?

Runners race for the same time, so distances are in the ratio of speeds. 'A beats B by 20 m in 100 m' means B runs 80 while A runs 100. To chain leads, multiply: if B beats C by 5 m, C reaches 80 × 0.95 = 76, so A wins by 24 m, not 25.

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

Multiply by 5/18, since 1 km is 1,000 m and 1 hour is 3,600 s. Easiest: remember 18 km/h equals 5 m/s and scale it, so 36 is 10, 54 is 15 and 72 is 20. Going back, multiply by 18/5, which is 3.6.

Are train and race questions still asked in CLAT?

CLAT 2019 had a train through a tunnel and a 100 m race as stand-alone questions. Since 2020 Quant comes as caselets, so speed questions arrive inside a passage about a journey or a timetable. The rules are identical; pull the lengths, speeds and directions into a table first.