A person covers the first half of a distance at 40 km/h and the second half at 60 km/h. What is the average speed for the whole journey?
Quantitative AptitudeTime Speed Distance AI confidence: 98%Asked 6/27/2026
AI-Verified Answer
Understanding the Problem
We need to find the average speed for the whole journey when:
- The first half of the distance is covered at \(40\) km/h
- The second half of the distance is covered at \(60\) km/h
Given Data
- Speed for first half \(= 40\) km/h
- Speed for second half \(= 60\) km/h
Formula to Use
Average speed is given by:
\[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
\]
When equal distances are covered at two different speeds \(a\) and \(b\), the average speed is:
\[
\text{Average Speed} = \frac{2ab}{a+b}
\]
Step-by-Step Solution
Step 1: Let the total distance be \(2d\)
Then each half of the distance is \(d\).
Step 2: Find time taken for each half
Time \(=\frac{\text{Distance}}{\text{Speed}}\)
Time for first half:
\[
t_1 = \frac{d}{40}
\]
Time for second half:
\[
t_2 = \frac{d}{60}
\]
Step 3: Find total time
\[
t = \frac{d}{40} + \frac{d}{60}
\]
Taking LCM \(= 120\):
\[
t = \frac{3d}{120} + \frac{2d}{120} = \frac{5d}{120} = \frac{d}{24}
\]
Step 4: Find average speed
\[
\text{Average Speed} = \frac{2d}{d/24}
\]
\[
\text{Average Speed} = 2d \times \frac{24}{d} = 48
\]
Final Answer
The average speed for the whole journey is \(48\) km/h.
Quick Summary
- Average speed is not the simple average of \(40\) and \(60\).
- Because the distances are equal, we use the harmonic mean formula.
\[
\text{Average Speed} = \frac{2 \times 40 \times 60}{40 + 60} = \frac{4800}{100} = 48 \text{ km/h}
\]
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