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Relative Speed

Relative Speed problems involve two objects moving towards each other or in the same direction. When moving towards each other, relative speed = sum of speeds; when moving in the same direction, relative speed = difference of speeds. These problems ask for meeting time, distance between them, or time to catch up.

10Worksheets
200+Practice Questions
IntermediateDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Relative Speed

Relative Speed problems involve two objects moving towards each other or in the same direction. When moving towards each other, relative speed = sum of speeds; when moving in the same direction, relative speed = difference of speeds. These problems ask for meeting time, distance between them, or time to catch up.

Prerequisites

Speed = Distance/Time concept Understanding of relative motion Addition and subtraction of speeds Basic arithmetic
Why This Matters: Relative Speed problems appear in 2-3 questions in SSC CGL and Banking PO exams. They test understanding of relative motion concepts.

How to Solve Relative Speed Problems

1

Step 1: Identify the direction of motion (towards or same direction)

2

Step 2: Calculate relative speed: towards = sum, same = difference

3

Step 3: Identify the distance to be covered

4

Step 4: Use formula: Time = Distance / Relative Speed

5

Step 5: For catch-up problems, distance = initial separation

6

Step 6: Calculate the required value

7

Step 7: Answer with appropriate units

Pro Strategy: Always determine whether objects are moving towards or away from each other. Towards = speeds add; same direction = speeds subtract. The time to meet or catch up is distance divided by relative speed.

Example Problem

Example: Two trains start from stations 300 km apart and move towards each other at 40 km/h and 60 km/h. When will they meet? Solution: Step 1: Moving towards each other Step 2: Relative speed = 40 + 60 = 100 km/h Step 3: Distance = 300 km Step 4: Time = 300 / 100 = 3 hours Answer: 3 hours

Pro Tips & Tricks

  • Towards each other: Rel Speed = v₁ + v₂
  • Same direction: Rel Speed = |v₁ - v₂|
  • Time to meet = Distance / (v₁ + v₂)
  • Time to catch up = Initial separation / (v₁ - v₂)
  • If starting from same point, distance = 0 for meeting
  • For trains crossing, total distance = sum of lengths

Shortcut Methods to Solve Faster

Meeting time = Distance / (v₁ + v₂)
Catch-up time = Gap / (v₁ - v₂)
If two trains cross a pole, time = train length / relative speed

Common Mistakes to Avoid

Adding speeds when moving same direction (should subtract)
Subtracting speeds when moving towards (should add)
Forgetting to convert units to be consistent

Exam Importance

Relative Speed is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
CAT
1-2 questions
INSURANCE
2-3 questions

Ready to Master Relative Speed?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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