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A person travels from X to Y at 40 km/h and returns at 60 km/h. What is the average speed for the entire journey?
48┬аkm/h
50┬аkm/h
52┬аkm/h
45┬аkm/h
48┬аkm/h
When a distance is covered at two different speeds for equal distances, the average speed is the harmonic mean of the speeds: 2uv/(u+v).
Speed from X to Y (v1) = 40 km/h, Speed from Y to X (v2) = 60 km/h
Average┬аSpeed=v1тАЛ+v2тАЛ2тЛЕv1тАЛтЛЕv2тАЛтАЛ
When a distance is covered at two different speeds for equal distances, the average speed is the harmonic mean of the speeds: 2uv/(u+v).
Students often fall into the trap of simply taking the arithmetic mean of the two speeds, i.e., (40+60)/2=50┬аkm/h, which is incorrect.
Identify Given Speeds
Note down the speed while traveling from X to Y as v1тАЛ=40┬аkm/h and the return speed as v2тАЛ=60┬аkm/h.
v1тАЛ=40┬аkm/h,v2тАЛ=60┬аkm/h
Apply Average Speed Formula for Equal Distances
Since the distance traveled in both directions is the same, use the standard harmonic mean formula for average speed.
Average┬аSpeed=v1тАЛ+v2тАЛ2v1тАЛv2тАЛтАЛ
Substitute the Values
Substitute v1тАЛ=40 and v2тАЛ=60 into the formula to compute the numerator and denominator.
Average┬аSpeed=40+602├Ч40├Ч60тАЛ
Calculate the Result
Simplify the expression to find the final average speed value in km/h.
Average┬аSpeed=1004800тАЛ=48┬аkm/h
A is correct because the calculated average speed for the round trip is 48 km/h.
This harmonic mean concept is frequently used in work-time problems involving pipes and cisterns or men and days.
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