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Time, Speed and Distance — REET Maths Notes

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This page covers REET maths' 'Time, Speed and Distance' topic as per the syllabus — unit conversion, average speed, relative speed, and the formulas for trains and boats-and-streams are explained through verified examples. This topic is included in the syllabus for both REET Level 1 and Level 2 maths papers, so getting the exact formulas and unit conversions right matters.

  • 0 questions in REET 2024 (syllabus-based notes)
  • Class 6–8 level
  • 8 min read
Verified 17 September 2026 · Source: BSER — REET आधिकारिक सिलेबस व 2024 प्रश्न-पत्र (मूल PDF; बोर्ड पोर्टल पर अब उपलब्ध नहीं)

How this topic is asked in REET

No direct question on 'Time, Speed and Distance' was found in the REET 2024 paper records. Even so, it's a regular part of the arithmetic section of the official BSER maths syllabus (Class 6–8 level), and sub-topics like trains and boats-and-streams are commonly asked in competitive exams generally. The notes below are based purely on the syllabus wording and standard formulas, with no reliance on any imagined 'previous question'.

Core formulas and unit conversion

Speed means distance covered per unit time: speed = distance ÷ time, so distance = speed × time, and time = distance ÷ speed. At the REET level, the most common mistake happens in unit conversion — to convert km/h to m/s, multiply by 5/18, and to convert m/s to km/h, multiply by 18/5.

Example: convert 72 km/h to m/s — 72 × 5/18 = 20 m/s. Similarly, convert 25 m/s to km/h — 25 × 18/5 = 90 km/h. Having this conversion memorised helps in every train- and race-related question.

Formulas worth knowing

Basic formula
speed = distance/time; distance = speed×time; time = distance/speed
km/h to m/s
value × 5/18
m/s to km/h
value × 18/5
Average speed (equal distance, different speeds x and y)
2xy/(x+y)
Relative speed — opposite directions
sum of both speeds
Relative speed — same direction
difference of both speeds
Boats and streams: with the current (downstream)
boat's speed + current's speed
Boats and streams: against the current (upstream)
boat's speed − current's speed

Worked examples on average speed and relative speed

Average speed is never simply the average of two speeds when the distance is equal and the time differs — the correct formula is 2xy/(x+y). Example: a person travels at 40 km/h while going, and at 60 km/h (over an equal distance) while returning, so the average speed for the whole trip = 2×40×60/(40+60) = 4800/100 = 48 km/h, not the simple average of 50 km/h.

Relative speed is used whenever two objects move at the same time. Example: two trains move in opposite directions at 60 km/h and 40 km/h, with lengths 100m and 150m. The time they take to cross each other = total distance ÷ relative speed. Relative speed = 60+40 = 100 km/h = 100×5/18 = 250/9 m/s. Total distance = 100+150 = 250m. Time = 250 ÷ (250/9) = 9 seconds.

Worked examples: trains and boats-and-streams

SituationSolution
A 150m long train crosses a pole in 9 seconds. Find the train's speed in km/h.speed = 150/9 = 50/3 m/s = (50/3)×18/5 = 60 km/h
A train crosses a 250m long platform in 20 seconds and crosses a pole in 10 seconds. Find the train's length.Let the length = L, speed = L/10; for the platform: (L+250)/20 = L/10 ⇒ L+250 = 2L ⇒ L = 250m
A boat's speed in still water is 10 km/h and the current's speed is 2 km/h. How long will it take to travel 24 km downstream?downstream speed = 10+2 = 12 km/h; time = 24/12 = 2 hours

Every value here has been solved and checked.

Questions of the 'early-late' type

Another common question type is one where the distance stays fixed, but a change in speed causes the arrival time to be early or late. Here, the equation is built by setting the difference in the times taken at the two speeds equal to the difference in minutes given in the question.

Example: a student walks from home to school at 6 km/h and arrives 10 minutes late; if she walks at 8 km/h instead, she arrives 5 minutes early. Find the distance from home to school. Solution: total time difference = 10+5 = 15 minutes = 1/4 hour. Let the distance = d, so d/6 − d/8 = 1/4. Taking the LCM as 24: 4d/24 − 3d/24 = d/24 = 1/4, so d = 6 km. Check: at 6 km/h, time for 6 km = 1 hour = 60 minutes; at 8 km/h, time = 45 minutes; the difference = 15 minutes, which matches the question.

How to teach this to children

Activity

Mark a fixed distance (say, 50 metres) on the school field and have students time themselves walking and running it with a stopwatch, then have them work out speed themselves as distance÷time — this turns the formula from something abstract into something measured and experienced.

Teaching aid

Using a bicycle or toy car with a measuring tape and stopwatch is a practical way to introduce the units of speed (m/s, km/h) in Class 6–7.

Common misconception

Students often assume average speed is simply the average of two speeds (like (40+60)/2=50), when the correct formula for equal distances is 2xy/(x+y) — this misconception needs checking repeatedly.

Assessment idea

Ask students 'how does relative speed change if two people walk towards each other, versus if they walk in the same direction?' and have them write a reasoned answer to check their understanding.

A trick worth remembering

Always multiply by 5/18 to go from km/h to m/s ('moving to a smaller unit needs a smaller multiplier' — 5/18 < 1), and multiply by 18/5 to go from m/s to km/h. Add speeds for opposite directions, subtract speeds for the same direction — that's the whole secret of relative speed.

Practice questions

Question 1

Convert 54 km/h into m/s.

  1. A10 m/s
  2. B18 m/s
  3. C20 m/s
  4. D15 m/s

Explanation

To convert km/h to m/s, multiply by 5/18: 54 × 5/18 = 15 m/s.

Question 2

A car covers 180 km in 3 hours. Find its speed in km/h.

  1. A45 km/h
  2. B90 km/h
  3. C60 km/h
  4. D50 km/h

Explanation

Speed = distance/time = 180/3 = 60 km/h.

Question 3

A man walking at 5 km/h covers a distance in 4 hours. If he walks at 8 km/h, how long will he take to cover the same distance?

  1. A3.5 घंटे
  2. B2.5 घंटे
  3. C3 घंटे
  4. D2 घंटे

Explanation

Distance = 5×4 = 20 km. Time at 8 km/h = 20/8 = 2.5 hours.

Question 4

Going speed is 30 km/h and return speed (equal distance) is 20 km/h. Find the average speed for the whole journey.

  1. A24 km/h
  2. B25 km/h
  3. C26 km/h
  4. D22 km/h

Explanation

Average speed = 2xy/(x+y) = 2×30×20/(30+20) = 1200/50 = 24 km/h (the simple average of 25 km/h is the wrong answer here).

Question 5

Two trains 120m and 180m long run on parallel tracks in opposite directions at 54 km/h and 36 km/h. Find the time taken to cross each other.

  1. A10 सेकंड
  2. B20 सेकंड
  3. C12 सेकंड
  4. D15 सेकंड

Explanation

Relative speed = 54+36 = 90 km/h = 90×5/18 = 25 m/s. Total distance = 120+180 = 300m. Time = 300/25 = 12 seconds.

Question 6

A train crosses a 250m platform in 20 seconds and a signal pole in 10 seconds. Find the length of the train.

  1. A300m
  2. B250m
  3. C150m
  4. D200m

Explanation

Let the length = L, so speed = L/10. Crossing the platform: (L+250)/20 = L/10 ⇒ L+250 = 2L ⇒ L = 250m.

Question 7

A thief runs at 8 km/h. A policeman chases him at 10 km/h when the thief is 100m ahead. In how much time will the policeman catch the thief?

  1. A6 मिनट
  2. B5 मिनट
  3. C2 मिनट
  4. D3 मिनट

Explanation

Relative speed (same direction) = 10−8 = 2 km/h = 2×5/18 = 5/9 m/s. Distance = 100m. Time = 100÷(5/9) = 180 seconds = 3 minutes.

Question 8

A boat's speed in still water is 12 km/h and stream speed is 3 km/h. Find the total time to travel 45 km downstream and return.

  1. A8 घंटे
  2. B9 घंटे
  3. C6 घंटे
  4. D7.5 घंटे

Explanation

Downstream speed = 12+3 = 15 km/h, time = 45/15 = 3 hours. Upstream speed = 12−3 = 9 km/h, time = 45/9 = 5 hours. Total time = 3+5 = 8 hours.

Question 9

Which is the most suitable teaching activity to explain the concept of 'speed' in Class 6?

  1. Aकेवल सूत्र चाल=दूरी/समय बोर्ड पर लिखकर याद करवाना
  2. Bमैदान में एक निश्चित दूरी नापकर विद्यार्थियों से चलने/दौड़ने का समय नपवाना और स्वयं चाल निकलवाना
  3. Cविद्यार्थियों को गतिविधि में शामिल न करना, केवल व्याख्यान देना
  4. Dबिना गतिविधि के सीधे पाठ्यपुस्तक के प्रश्न हल करवाना

Explanation

Measuring speed themselves promotes experiential learning, which makes the abstract formula meaningful and memorable afterward — this is far more effective than rote learning alone.

Question 10

A bus travelling at 60 km/h covers how much distance in 45 minutes?

  1. A30 km
  2. B60 km
  3. C45 km
  4. D50 km

Explanation

45 minutes = 0.75 hours. Distance = speed×time = 60×0.75 = 45 km.

Frequently asked questions

How many questions come from 'Time, Speed and Distance' in the REET exam?+

No direct question from this topic was found on record in REET 2024, but it is included in the official BSER maths syllabus, so preparing it shouldn't be skipped.

What's the formula for converting km/h to m/s?+

Multiply the km/h value by 5/18 to get the value in m/s; to convert back the other way, multiply by 18/5.

What's the correct way to find average speed?+

If an equal distance is travelled at two different speeds x and y, the average speed = 2xy/(x+y), not (x+y)/2 — this is the most common mistake in REET questions.

What do downstream and upstream mean in boats-and-streams questions?+

Downstream means travelling with the current (boat's speed + current's speed), and upstream means travelling against the current (boat's speed − current's speed).

How do you solve 'early-late' type time-distance questions?+

The distance always stays fixed; you build an equation (d/speed1 − d/speed2 = time difference) by setting the difference in times taken at two different speeds equal to the given early/late minutes, and then solve for the distance.

Read next

Time and Work — REET Notes

Previous topic: read about the concept and formulas of time and work.

Lines and Angles — REET Notes

Next topic: read about the concept and formulas of lines and angles.

REET Syllabus 2024

See the complete official REET Level 1 and Level 2 syllabus, subject-wise.

REET 2024 Solved Papers

Read the REET 2024 previous papers with answers and explanations.

Official Sources

  1. BSER — REET आधिकारिक सिलेबस व 2024 प्रश्न-पत्र (मूल PDF; बोर्ड पोर्टल पर अब उपलब्ध नहीं)

Change Log

  • 17 September 2026 — English page published — mirrors the fact-checked Hindi page, independently bilingual-accuracy checked