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Time, Speed, and Distance – Basic Formulas Made Simple for Students

Understanding Time, Speed, and Distance (TSD) is essential for success in quantitative aptitude tests and competitive exams. The topic becomes easy once you know the simple relationships between these three concepts.

Let’s break it down in the simplest possible way.

What is Time, Speed, and Distance?

These three are related through one basic formula that can be rearranged as needed.

  • Speed = Distance ÷ Time

  • Distance = Speed × Time

  • Time = Distance ÷ Speed

You can easily remember this using the TSD triangle —
Write Distance (D) at the top, and Speed (S) and Time (T) at the bottom corners.
Cover the one you need to find, and the formula appears automatically!

Important Unit Conversions

To solve questions correctly, keep units consistent.

  • 1 km/hr = 5/18 m/s

  • 1 m/s = 18/5 km/hr

Average Speed

When the total distance is the same for both parts of the journey:
Average Speed = (2 × S₁ × S₂) ÷ (S₁ + S₂)

When distances are different:
Average Speed = Total Distance ÷ Total Time

Relative Speed

When two objects move towards each other (opposite directions):
Relative Speed = S₁ + S₂

When they move in the same direction:
Relative Speed = |S₁ − S₂|

Train-Based Problems

  1. Crossing a Pole or Person
    Time = Train Length ÷ Speed

  2. Crossing a Platform
    Time = (Train Length + Platform Length) ÷ Speed

  3. Two Trains Crossing Each Other
    Time = (Length₁ + Length₂) ÷ Relative Speed

Boat and Stream Formulas

  • Downstream Speed = Boat Speed + Stream Speed

  • Upstream Speed = Boat Speed − Stream Speed

  • Speed in Still Water = (Downstream + Upstream) ÷ 2

  • Speed of Stream = (Downstream − Upstream) ÷ 2

Quick Tip for Students

Always:

  • Keep units the same before solving (convert km/h to m/s if needed).

  • Remember the triangle method (D–S–T) for quick recall.

  • Use the formula that matches the given question type (distance, time, or average speed).

Mastering these simple formulas will make Time, Speed, and Distance one of the easiest and most scoring topics in your aptitude exams!

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