Question

Abdul, while driving to school, computes the average speed for his trip to be 20 km h⁻¹. On his return trip along the same route, there is less traffic and the average speed is 30 km h⁻¹. What is the average speed for Abdul’s trip?

Answer 1

Case I: While driving to school

Average speed of Abdul’s trip = 20 km/h

Total distance = Distance travelled to reach school = d

Let total time taken = t₁

…(i)

Case II: While returning from school

Total distance = Distance travelled while returning from school = d

Now,total time taken = t₂

$$\begin{gathered} 30=\frac{d}{t_2} \\ {t}_2=\frac{d}{30}.....\left(ii\right) \end{gathered}$$

Where,

Total distance covered in the trip = d + d = 2d

Total time taken, t = Time taken to go to school + Time taken to return to school

= t₁ + t₂

From equations (i) and (ii),

$$\begin{gathered} \mathrm{Average}\mathrm{Speed}=\frac{2\mathrm{d}}{{\displaystyle \frac{\mathrm{d}}{20}+\frac{\mathrm{d}}{30}}}=\frac{2}{{\displaystyle \frac{3+2}{60}}} \\ \mathrm{Average}\mathrm{Speed}=\frac{120}{5}=24\mathrm{km}/\mathrm{h} \end{gathered}$$

Hence, the average speed for Abdul’s trip is 24 km/h.