A train travels from City A to City B at a speed of 120 km/h and returns at 80 k

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Question: A train travels from City A to City B at a speed of 120 km/h and returns at 80 km/h. What is the average speed for the entire journey?

Options:

Correct Answer: 96 km/h

Solution:

Average Speed = 2ab / (a + b) = 2 * 120 * 80 / (120 + 80) = 96 km/h.

A train travels from City A to City B at a speed of 120 km/h and returns at 80 km/h. What is the average speed for the entire journey?

A train travels from City A to City B at a speed of 120 km/h and returns at 80 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 120 km/h (let's call this 'a'), and the speed from City B back to City A is 80 km/h (let's call this 'b').
Step 2: Use the formula for average speed when traveling the same distance at two different speeds: Average Speed = 2ab / (a + b).
Step 3: Substitute the values of 'a' and 'b' into the formula: Average Speed = 2 * 120 * 80 / (120 + 80).
Step 4: Calculate the denominator: 120 + 80 = 200.
Step 5: Calculate the numerator: 2 * 120 * 80 = 19200.
Step 6: Divide the numerator by the denominator: 19200 / 200 = 96.
Step 7: The average speed for the entire journey is 96 km/h.

Average Speed Calculation – The average speed for a round trip is calculated using the formula 2ab / (a + b), where 'a' is the speed in one direction and 'b' is the speed in the opposite direction.
Speed and Distance Relationship – Understanding that average speed is not simply the arithmetic mean of the two speeds when distances are equal.