A man covers half of his journey at 6 km/hr and the remaining half at 3 km/hr. His average speed is _____?
- 4 km/hr
- 9 km/hr
- 4.5 km/hr
- None
Explanation
Let the total distance be x km.
The man covers half the distance at 6 km/hr, so the time taken to cover this half is:
Time = Distance / Speed = (x/2) / 6 = x/12
The man covers the remaining half at 3 km/hr, so the time taken to cover this half is:
Time = Distance / Speed = (x/2) / 3 = x/6
The total time taken to cover the entire distance is the sum of the times taken to cover each half:
Total Time = x/12 + x/6
To add these fractions, we need a common denominator, which is 12. So we can rewrite the fractions as:
Total Time = x/12 + 2x/12 = 3x/12 = x/4
Now, we can find the average speed:
Average Speed = Total Distance / Total Time = x / (x/4) = 4 km/hr
So, the correct answer is: 4 km/hr
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