Time, Speed and Distance Cheat Sheet

Time, Speed and Distance Cheat Sheet

Quick Revision

Speed, distance and time are linked by one relationship: distance = speed × time. Everything else in this topic follows from it.

Ready to practise? Take the Time, Speed and Distance quiz

1. Basic Formulas

Speed    = Distance / Time
Distance = Speed × Time
Time     = Distance / Speed

Speed and time are inversely proportional for a fixed distance: go faster, take less time.

2. Unit Conversion

km/hr → m/s :  multiply by 5/18
m/s → km/hr :  multiply by 18/5

Example

72 km/hr = 72 × 5/18 = 20 m/s.

3. Average Speed

Average speed = Total distance / Total time

For equal distances at speeds x and y:

Average speed = 2xy / (x + y)

This is the harmonic mean, not (x + y)/2.

4. Relative Speed

Use relative speed whenever two bodies move at the same time (overtaking or meeting).

5. Train Problems

A train must cover its own length plus the length of whatever it passes.

Example

A 150 m train at 20 m/s crosses a 250 m platform in:

(150 + 250) / 20 = 400 / 20 = 20 seconds

6. Boats and Streams

Let the boat's speed in still water be b and the stream's speed be s.

Downstream speed = b + s
Upstream speed   = b − s

Boat speed  = (downstream + upstream) / 2
Stream speed = (downstream − upstream) / 2

7. Exam Quick Tips

• Keep units consistent — convert km/hr to m/s with × 5/18 before mixing with metres and seconds.
• For equal distances, average speed is 2xy/(x+y), never the simple average.
• Same direction → subtract speeds; opposite → add.
• A train crossing a platform covers train length + platform length.

Keep revising with the rest of the Maths section:

• All Maths topics
• Time and Work Cheat Sheet
• Average Cheat Sheet

How this was made: Drafted with AI assistance; spot-checked by the editor on 31 October 2026.