JEE Main 2023 · 30 January · evening · Single correct · +4 / −1
A vehicle travels 4 km with speed of 3 km / h and another 4 km with speed of 5 km / h, then its average speed is
- (a) 3.75 km / h
- (b) 4.25 km / h
- (c) 3.50 km / h
- (d) 4.00 km / h
Answer and solution
Answer (a) 3.75 km / h
Solution
Physics sir · 3 steps
Equal distances, not equal times: find the time for each leg first, then divide total distance by total time.
- Time for each leg. The first 4 km at 3 km/h takes 4/3 h. The second 4 km at 5 km/h takes 4/5 h.
- Total time. 4/3 + 4/5 = (20 + 12)/15 = 32/15 h. The total distance is 8 km.
v_(avg) = (total distance)/(total time) = 8/(32/15) = 120/32 = 3.75 km/h
- So. The average speed is 3.75 km/h, option (a). It sits closer to 3 than to 5 because the vehicle spends more time on the slow leg.
The idea to keep. For equal distances at speeds v₁ and v₂, the average speed is 2v₁v₂/(v₁+v₂), not their simple mean. A plain average works only for equal times.
Answer from the NTA final answer key. Solution by PrepWiser.