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

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

Options:

  1. 72 km/h
  2. 75 km/h
  3. 78 km/h
  4. 80 km/h

Correct Answer: 72 km/h

Solution: 

Average speed = 2ab / (a + b) = 2 × 90 × 60 / (90 + 60) = 5400 / 150 = 72 km/h.

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

Practice Questions

Q1
A train travels from City A to City B at a speed of 90 km/h and returns at a speed of 60 km/h. What is the average speed for the entire journey?
  1. 72 km/h
  2. 75 km/h
  3. 78 km/h
  4. 80 km/h

Questions & Step-by-Step Solutions

A train travels from City A to City B at a speed of 90 km/h and returns at a speed of 60 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 90 km/h (let's call this 'a') and the speed from City B back to City A is 60 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 × 90 × 60 / (90 + 60).
  • Step 4: Calculate the numerator: 2 × 90 × 60 = 10800.
  • Step 5: Calculate the denominator: 90 + 60 = 150.
  • Step 6: Divide the numerator by the denominator 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 2ab / (a + b), where 'a' is the speed for the first leg and 'b' is the speed for the return leg.
  • Speed and Distance Relationship – Understanding that average speed is not simply the arithmetic mean of the two speeds when distances are equal.
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