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?
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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.
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