Question

A train covers a certain distance at 60 km/h and returns at 40 km/h. The average speed for the entire journey is:

• A. 48 km/h
• B. 50 km/h
• C. 52 km/h
• D. 54 km/h

Hint:

For equal distances, never take the simple average of speeds—always use the harmonic mean formula.

Answer 1

The Correct Option is A

Step 1: Recall the average speed formula.
When equal distances are covered at different speeds, the average speed is given by:
\[ \text{Average speed} = \frac{2ab}{a+b} \] where \( a \) and \( b \) are the two speeds.
Step 2: Substitute the given values.
Here, \( a = 60 \) km/h and \( b = 40 \) km/h.
\[ \text{Average speed} = \frac{2 \times 60 \times 40}{60 + 40} \]
Step 3: Simplify the expression.
\[ \text{Average speed} = \frac{4800}{100} = 48 \text{ km/h} \]
Step 4: Conclusion.
The average speed for the entire journey is 48 km/h.