Question

Rahul, while driving to school, computes the average speed for his trip to be 30 km/hr. On his return trip along the same route, there is less traffic and the average speed is 40 km/hr. What is the average speed for the entire trip?

Answer 1

Answer:

Let us assume :

• The distance from home to school is x.
• The total distance travelled by Rahul to school and back is 2x.
• The average speed from A to B = v1 = 30 km/h
• The average speed from B to A = v2 = 40 km/h
• Time taken to travel from A to B = t1
• Time taken to travel from B to A = t2

We know that, Distance = Speed×Time

Case 1 : From A to B

⇒ Distance = v1×t1 = 30t1

⇒ Time = x/30 s

Case 2 : From B to A

⇒ Distance = v2×t2 = 40t2

⇒ Time = x/40 s

Now, Average Speed = Total Distance/Total Time

⇒ v_avg = 2x/(x/30 + x/40)

⇒ v_avg = 2x/[(30x+40x)/1,200)

⇒ v_avg = 2x/(7x/1,20)

⇒ v_avg = 2x × 1,20/7x

⇒ v_avg = (2×120)/7

⇒ v_avg = 34.28 km/h

Hence, the average speed for the entire trip = 34.28 km/h.