The Question

A car travels from City A to City B at 40 km/h and returns back at 60 km/h. What is the average speed for the entire journey?

Method 1 (Traditional)

  1. Assume the distance between A and B is $d$.
  2. Time taken for forward journey ($t_1$) = $\frac{d}{40}$.
  3. Time taken for return journey ($t_2$) = $\frac{d}{60}$.
  4. Total Distance = $2d$.
  5. Total Time = $\frac{d}{40} + \frac{d}{60} = \frac{3d + 2d}{120} = \frac{5d}{120} = \frac{d}{24}$.
  6. Average Speed = $\frac{\text{Total Distance}}{\text{Total Time}} = \frac{2d}{d/24} = 2 \times 24 = \mathbf{48 \text{ km/h}}$.

Method 2 (Booster Shortcut) ⚡

When the distance covered is the same for both speeds ($x$ and $y$), use the Harmonic Mean Formula:

$$\text{Average Speed} = \frac{2xy}{x + y}$$

Calculation:

  • $x = 40, y = 60$
  • $\text{Avg Speed} = \frac{2 \times 40 \times 60}{40 + 60}$
  • $\text{Avg Speed} = \frac{4800}{100} = \mathbf{48 \text{ km/h}}$

Correct Answer: A) 48 km/h

CTA: Never miss a shortcut! [Join our WhatsApp Channel] for daily challenges and "Booster" tips delivered to your phone.