Question

If a man covers one-third distance at speeds 10 km/h, 20 km/h, and 60 km/h, find the average speed.

Hint:

For equal distances, average speed is not the arithmetic mean; always use total distance divided by total time.

Answer 1

Step 1: Assume total distance.
Let the total distance be \(3d\).
Then each part is \(d\).
Step 2: Calculate time taken for each part.
\[ \text{Time}_1 = \frac{d}{10},\quad \text{Time}_2 = \frac{d}{20},\quad \text{Time}_3 = \frac{d}{60} \]
Step 3: Find total time.
\[ \text{Total time} = d\left(\frac{1}{10} + \frac{1}{20} + \frac{1}{60}\right) = d\left(\frac{6 + 3 + 1}{60}\right) = \frac{d}{6} \]
Step 4: Calculate average speed.
\[ \text{Average speed} = \frac{3d}{d/6} = 18 \text{ km/h} \]
Step 5: Conclusion.
The average speed is 18 km/h.