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Introduction
In aptitude tests, you’ll often face problems involving average speed. Unlike normal averages, average speed is not simply the average of the two speeds.
Instead, it follows a special formula when the same distance is traveled at two different speeds.
Pattern: Average Speed
Pattern: Average Speed
If a person covers the same distance at two speeds, say x and y,
Average Speed = (2xy) ÷ (x + y)
This formula comes from the idea that average speed is Total Distance ÷ Total Time.
Step-by-Step Example
Question
A person travels from town A to town B at 40 km/h and returns at 60 km/h. What is the average speed for the whole trip?
Options:
- A. 45 km/h
- B. 48 km/h
- C. 50 km/h
- D. 52 km/h
Solution
-
Step 1: Identify speeds
Speeds given = 40 km/h and 60 km/h. -
Step 2: Apply correct formula
Since the distance is the same, use:
Average Speed = (2 × 40 × 60) ÷ (40 + 60) -
Step 3: Compute the result
= 4800 ÷ 100 = 48 km/h -
Final Answer:
48 km/h → Option B -
Quick Check:
Total distance = 2d
Total time = d/40 + d/60 = (5d/120) = d/24
Avg speed = 2d ÷ (d/24) = 48 km/h → Correct ✅
Quick Variations
- 1. If the distances are not equal, use Average Speed = Total Distance ÷ Total Time.
- 2. For three equal distances with speeds x, y, z → Average Speed = (3xyz) ÷ (xy + yz + zx).
Trick to Always Use
- Same distance: Use (2xy) ÷ (x + y).
- Different distance: Use Total Distance ÷ Total Time.
- 3 equal distances: Use the 3-term formula directly.
Summary
The Average Speed pattern is very common in aptitude exams. Always remember:
- Equal distance (2 speeds): (2xy) ÷ (x + y)
- Equal distance (3 speeds): (3xyz) ÷ (xy + yz + zx)
- Unequal distance: Total Distance ÷ Total Time
Memorize these formulas to save time in exams.