A train travels from City A to City B at a speed of 75 km/h and returns at 60 km

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Question: A train travels from City A to City B at a speed of 75 km/h and returns at 60 km/h. What is the average speed for the entire journey?

Options:

Correct Answer: 65 km/h

Solution:

Average Speed = 2ab / (a + b) = 2(75)(60) / (75 + 60) = 2(4500) / 135 = 66.67 km/h.

A train travels from City A to City B at a speed of 75 km/h and returns at 60 km/h. What is the average speed for the entire journey?

A train travels from City A to City B at a speed of 75 km/h and returns at 60 km/h. What is the average speed for the entire journey?

Step 1: Identify the speeds for each part of the journey. The speed from City A to City B is 75 km/h, and the speed for the return trip from City B to City A is 60 km/h.
Step 2: Use the formula for average speed when the distances are the same. The formula is Average Speed = 2ab / (a + b), where 'a' is the speed to City B (75 km/h) and 'b' is the speed back to City A (60 km/h).
Step 3: Substitute the values into the formula: Average Speed = 2(75)(60) / (75 + 60).
Step 4: Calculate the numerator: 2(75)(60) = 2 * 4500 = 9000.
Step 5: Calculate the denominator: 75 + 60 = 135.
Step 6: Divide the numerator by the denominator: 9000 / 135 = 66.67.
Step 7: Conclude that the average speed for the entire journey is 66.67 km/h.

Average Speed Calculation – The average speed for a round trip is calculated using the formula 2ab / (a + b), where 'a' and 'b' are the speeds in each direction.
Harmonic Mean – The average speed in this scenario is a type of harmonic mean, which is used when dealing with rates or speeds.