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If the distance between A and B is 1253 Km. From A, Chaman goes to B with speed 93 km/h and return to A with the speed 95 km/h. Find the average speed of Chaman. (rounded off to two decimal place)
93.99 km/h
90.46 km/h
103.98 km/h
94.47 km/h
93.99 km/h
Since the distance is the same for both legs of the journey, the total distance (1253 km) is irrelevant. Use the harmonic mean of the two speeds.
Distance between A and B = 1253 km, Speed from A to B (v1) = 93 km/h, Speed from B to A (v2) = 95 km/h.
VavgтАЛ=v1тАЛ+v2тАЛ2├Чv1тАЛ├Чv2тАЛтАЛ
Since the distance is the same for both legs of the journey, the total distance (1253 km) is irrelevant. Use the harmonic mean of the two speeds.
Many students try to calculate the total time by dividing the total round-trip distance (2506 km) by the average of the speeds, or attempt to include the total distance (1253 km) in the formula, which is unnecessary.
Identify Constants
Identify the forward speed v1тАЛ=93 km/h and return speed v2тАЛ=95 km/h.
v1тАЛ=93,v2тАЛ=95
Apply Average Speed Formula
Since distance is constant, use the harmonic mean formula for average speed.
VavgтАЛ=93+952├Ч93├Ч95тАЛ
Calculate Values
Calculate the numerator 2├Ч93├Ч95=17670 and the denominator 93+95=188.
VavgтАЛ=18817670тАЛ
Final Division and Rounding
Divide 17670 by 188 to get approximately 93.98936, which rounds to 93.99 km/h.
VavgтАЛтЙИ93.99
A is correct because the harmonic mean of 93 km/h and 95 km/h is approximately 93.99 km/h.
This harmonic mean shortcut is extremely useful in Physics for calculating average velocity in constant-distance round-trip problems, saving time on calculating total time.
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