A train travels from City X to City Y at a speed of 100 km/h and returns at 80 k

₹0.0

Question: A train travels from City X to City Y at a speed of 100 km/h and returns at 80 km/h. What is the average speed for the entire journey?

Options:

Correct Answer: 85 km/h

Solution:

Average speed = 2ab / (a + b) = 2 × 100 × 80 / (100 + 80) = 16000 / 180 = 88.89 km/h.

A train travels from City X to City Y at a speed of 100 km/h and returns at 80 km/h. What is the average speed for the entire journey?

A train travels from City X to City Y at a speed of 100 km/h and returns at 80 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 X to City Y is 100 km/h (let's call this 'a'), and the speed from City Y back to City X is 80 km/h (let's call this 'b').
Step 2: Use the formula for average speed when the distances are the same: Average speed = 2ab / (a + b).
Step 3: Substitute the values of 'a' and 'b' into the formula: Average speed = 2 × 100 × 80 / (100 + 80).
Step 4: Calculate the numerator: 2 × 100 × 80 = 16000.
Step 5: Calculate the denominator: 100 + 80 = 180.
Step 6: Divide the numerator by the denominator: 16000 / 180 = 88.89.
Step 7: The average speed for the entire journey is 88.89 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.
Harmonic Mean – The average speed in this scenario is a specific case of the harmonic mean, which is used when dealing with rates.