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A car covers a distance of 120 km at 60 km/h and returns at 40 km/h. What is the average speed?
48┬аkm/h
50┬аkm/h
45┬аkm/h
55┬аkm/h
48┬аkm/h
For equal distances covered at two different speeds, use the harmonic mean formula: x+y2xyтАЛ, which eliminates the need to calculate actual distance.
Distance d = 120 km, Outward speed v1 = 60 km/h, Return speed v2 = 40 km/h
Average┬аSpeed=v1тАЛ+v2тАЛ2v1тАЛv2тАЛтАЛ
For equal distances covered at two different speeds, use the harmonic mean formula: x+y2xyтАЛ, which eliminates the need to calculate actual distance.
Students often incorrectly calculate the average speed as the arithmetic mean of the two speeds ((60+40)/2=50), ignoring the time spent at each speed.
Identify Given Parameters
Note the outward speed v1тАЛ=60┬аkm/h and return speed v2тАЛ=40┬аkm/h for the equal distance of 120┬аkm each way.
v1тАЛ=60┬аkm/h,v2тАЛ=40┬аkm/h
Apply Average Speed Formula
Since the distance traveled going and returning is equal, we apply the standard shortcut formula for average speed: Average┬аSpeed=v1тАЛ+v2тАЛ2v1тАЛv2тАЛтАЛ
Average┬аSpeed=v1тАЛ+v2тАЛ2v1тАЛv2тАЛтАЛ
Calculate the Result
Substitute the values of v1тАЛ and v2тАЛ into the formula: Average┬аSpeed=60+402├Ч60├Ч40тАЛ=1004800тАЛ=48┬аkm/h
Average┬аSpeed=1004800тАЛ=48┬аkm/h
A is correct because the average speed calculated using the harmonic formula is 48 km/h.
This shortcut is widely applicable in problems involving round trips, average rates, and work-time efficiencies.
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