Question

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

Answer 1

Solution :

Let the Distance at the school be x.

i) While driving to school,average speed is 20 km/h. Let the time taken be $\sf{t}_{1}$

★ Speed = Distance/Time

→ 20 = $\sf\dfrac{x}{t}_{1}$

→ $\sf{t}_{1} = \dfrac{x}{20}$ hrs

ii) While returning, the average speed is 30 km/h. Let the time taken be $\sf{t}_{2}$

★ Speed = Distance/Time

→ 30 = $\sf\dfrac{x}{t}_{2}$

→ $\sf{t}_{2} = \dfrac{x}{30}$ hrs

• Total Distance Covered = Going + Return

→ x + x = 2x km

• Total Time taken = $\sf{t}_{1} + {t}_{2}$

→ $\sf \dfrac{x}{20}\ +\ \dfrac{x}{30}$

→ $\sf\dfrac{3x + 2x }{60}$

→ $\sf\cancel\dfrac{5x}{60}$

→ $\sf\dfrac{x}{12}$ hrs

Now,

★ Average Speed = Total distance covered/Total time taken

→ $\sf\dfrac{2x \times\: 12}{x}$

→ $\sf\cancel\dfrac{24x}{x}$

→ 24 km/h

$\therefore$ Average speed for Abdul's trip is 24 kilometers per hour.