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Average Speed

Average Speed problems involve calculating the overall speed for a journey covering different segments at different speeds. The formula depends on whether the segments cover equal distances or equal times. For equal distances, average speed is the harmonic mean; for equal times, it's the arithmetic mean.

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 Average Speed

Average Speed problems involve calculating the overall speed for a journey covering different segments at different speeds. The formula depends on whether the segments cover equal distances or equal times. For equal distances, average speed is the harmonic mean; for equal times, it's the arithmetic mean.

Prerequisites

Average concept Harmonic mean formula Distance = Speed × Time Weighted average principles
Why This Matters: Average Speed problems appear in 2-3 questions in SSC CGL and Banking PO exams. They test understanding of weighted averages in speed contexts.

How to Solve Average Speed Problems

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Step 1: Identify the scenario (equal distances or equal times)

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Step 2: For equal distances: Average Speed = (2 × v₁ × v₂) / (v₁ + v₂)

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Step 3: For equal times: Average Speed = (v₁ + v₂) / 2

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Step 4: For multiple segments, extend formulas accordingly

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Step 5: Calculate using given speeds

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Step 6: Round to required decimal places

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Step 7: Answer with speed in km/h or m/s

Pro Strategy: For equal distances, average speed is always less than the arithmetic mean. For equal times, average speed equals the arithmetic mean. Never simply average the speeds unless times are equal.

Example Problem

Example: A person travels from A to B at 40 km/h and returns at 60 km/h. What is the average speed? Solution: Step 1: Equal distances (A to B and B to A) Step 2: Average Speed = (2 × 40 × 60) / (40 + 60) = (4800) / 100 = 48 km/h Answer: 48 km/h

Pro Tips & Tricks

  • Equal distances formula: Avg = 2ab/(a+b) (harmonic mean)
  • Equal times formula: Avg = (a+b)/2 (arithmetic mean)
  • For three equal distances: Avg = 3abc/(ab+bc+ca)
  • The average speed is not the average of speeds unless times are equal
  • For a journey with uphill and downhill, use equal distance formula

Shortcut Methods to Solve Faster

Two speeds: harmonic mean for equal distances
Two speeds: arithmetic mean for equal times
If one speed is double the other, average speed for equal distances = (4/3) × slower

Common Mistakes to Avoid

Averaging speeds directly without checking the scenario
Using equal distance formula for equal times (and vice versa)
Forgetting that total distance = 2 × one-way distance

Exam Importance

Average 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 Average 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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