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Answer :
Final answer:
The average speed of the car which travels to a point and back at different speeds is calculated using the harmonic mean, not the arithmetic mean. In this case, the average speed is 34.3km/h.
Explanation:
This question, in essence, is about determining the average speed of a car that travels a distance from point A to B and then back to A at different speeds. The average speed is calculated by dividing the total distance traveled by the total time taken.
However, a vital point to note is how we should calculate the average speed when the trip consists of two equal distances covered at different speeds. In such cases, the harmonic mean is employed. The harmonic mean for two speeds, v1 and v2, can be found by using the formula:
2*v1*v2 / (v1+v2).
Now, substituting the given, 40km/h for v1 and 30km/h for v2, you get the average speed as:
2*40*30 / (40+30) = 2400/70 = 34.3km/h. Therefore, the correct answer is a. 34.3
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