Abdul, while driving to school, computes the average speed for his trip to be 20 kmh^-1. On his return trip along the same route, there is less traffic and the average speed is 30 kmh^-1. What is the average speed for Abdul's trip?

Distance travelled to reach the school = distance travelled to reach home = d

Time taken to reach school = t₁

Time taken to reach home = t₂

Average speed = $\dfrac{\text{total distance travelled}}{\text{total time taken}}$

On going to school :

20 = $\dfrac{\text{d}}{\text{t}_1}$ or

t₁ = $\dfrac{\text{d}}{20}$

On return trip :

30 = $\dfrac{\text{d}}{\text{t}_2}$ or

t₂ = $\dfrac{\text{d}}{30}$

Now, the average speed for the entire trip

= $\dfrac{\text{d+d}}{\text{t}$1 + \text{t}2}

= $\dfrac{\text{2d}}{\dfrac{\text{d}}{20} + \dfrac{\text{d}}{30}}$

= $\dfrac{\text{2d}}{\dfrac{\text{3d + 2d}}{60}}$

= $\dfrac{\text{2d} \times {60}}{5\text{d}}$

= 24 kmh^-1

∴ Abdul's average speed for the entire trip is 24 kmh^-1.