A train travels from City A to City B at a speed of 60 km/h and returns at 90 km

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Question: A train travels from City A to City B at a speed of 60 km/h and returns at 90 km/h. What is the average speed for the entire journey?

Options:

Correct Answer: 72 km/h

Solution:

Average Speed = 2 * (Speed1 * Speed2) / (Speed1 + Speed2) = 2 * (60 * 90) / (60 + 90) = 72 km/h.

A train travels from City A to City B at a speed of 60 km/h and returns at 90 km/h. What is the average speed for the entire journey?

A train travels from City A to City B at a speed of 60 km/h and returns at 90 km/h. What is the average speed for the entire journey?

Step 1: Identify the speeds for the two parts of the journey. The speed from City A to City B is 60 km/h (Speed1) and the speed from City B to City A is 90 km/h (Speed2).
Step 2: Use the formula for average speed when the distances are the same: Average Speed = 2 * (Speed1 * Speed2) / (Speed1 + Speed2).
Step 3: Plug in the values into the formula: Average Speed = 2 * (60 * 90) / (60 + 90).
Step 4: Calculate the product of the speeds: 60 * 90 = 5400.
Step 5: Calculate the sum of the speeds: 60 + 90 = 150.
Step 6: Substitute these values back into the formula: Average Speed = 2 * 5400 / 150.
Step 7: Calculate 2 * 5400 = 10800.
Step 8: Divide 10800 by 150 to find the average speed: 10800 / 150 = 72 km/h.

Average Speed Calculation – The average speed for a round trip is calculated using the formula for two speeds, which accounts for the different 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.