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A person covers a distance of 100 km. He travels the first 50 km at 25 km/h and the next 50 km at 50 km/h. Find average speed.
33.33┬аkm/h
37.5┬аkm/h
30┬аkm/h
40┬аkm/h
33.33┬аkm/h
For equal distances covered at two different speeds, use the harmonic mean formula 2v1тАЛv2тАЛ/(v1тАЛ+v2тАЛ) to save calculation time.
Total distance = 100 km, First distance = 50 km at 25 km/h, Second distance = 50 km at 50 km/h
vavgтАЛ=v1тАЛ+v2тАЛ2├Чv1тАЛ├Чv2тАЛтАЛ
For equal distances covered at two different speeds, use the harmonic mean formula 2v1тАЛv2тАЛ/(v1тАЛ+v2тАЛ) to save calculation time.
Students often calculate the simple arithmetic mean of the two speeds (25+50)/2=37.5┬аkm/h, ignoring that more time is spent at the slower speed.
Calculate Time for Each Segment
Compute the time taken for the first and second halves of the journey using time equals distance divided by speed.
t1тАЛ=2550тАЛ=2┬аh,t2тАЛ=5050тАЛ=1┬аh
Find Total Distance and Total Time
Add the individual distances and time durations to find the totals for the complete trip.
Total┬аDistance=100┬аkm,Total┬аTime=2+1=3┬аh
Calculate Average Speed
Divide total distance by total time to arrive at the final average speed value.
vavgтАЛ=3100тАЛ=33.33┬аkm/h
A is correct because the average speed is the total distance divided by the total time, yielding 100/3=33.33 km/h.
Questions involving relative motion and average speed often appear in railway and aptitude exams, requiring quick identification of equal distance vs. equal time scenarios.
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