Question

A car travels at 60 km/h for half the distance and 80 km/h for the other half. What is the average speed for the entire journey? 
 

• A. $\frac{200}{3}$ km/h
• B. $\frac{480}{7}$ km/h
• C. 70 km/h
• D. 72 km/h

Hint:

For equal distances, average speed = harmonic mean: $\frac{2v_1v_2}{v_1 + v_2}$.

Answer 1

The Correct Option is B

- Step 1: Assume total distance - Let the total distance = $2d$ km. Each half = $d$ km. 
- Step 2: Time for first half - Speed = 60 km/h: \[ t_1 = \frac{d}{60} \] 
- Step 3: Time for second half - Speed = 80 km/h: \[ t_2 = \frac{d}{80} \] 
- Step 4: Total time - \[ T = t_1 + t_2 = \frac{d}{60} + \frac{d}{80} = d \left( \frac{4}{240} + \frac{3}{240} \right) = \frac{7d}{240} \] 
- Step 5: Average speed formula - \[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{2d}{\frac{7d}{240}} = \frac{2d \times 240}{7d} = \frac{480}{7} \ \text{km/h} \] 
- Step 6: Conclusion - Average speed = $\frac{480}{7}$ km/h, matching option (2).