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A train travels from city X to city Y at a speed of 80 km/h and returns at a spe

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Question: A train travels from city X to city Y at a speed of 80 km/h and returns at a speed of 60 km/h. What is the average speed for the entire journey?

Options:

  1. 70 km/h
  2. 72 km/h
  3. 75 km/h
  4. 78 km/h

Correct Answer: 72 km/h

Solution: 

Average speed = 2xy / (x + y) where x = 80 and y = 60. Average speed = 2 * 80 * 60 / (80 + 60) = 72 km/h.

A train travels from city X to city Y at a speed of 80 km/h and returns at a spe

Practice Questions

Q1
A train travels from city X to city Y at a speed of 80 km/h and returns at a speed of 60 km/h. What is the average speed for the entire journey?
  1. 70 km/h
  2. 72 km/h
  3. 75 km/h
  4. 78 km/h

Questions & Step-by-Step Solutions

A train travels from city X to city Y at a speed of 80 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 X to city Y is 80 km/h (let's call this x), and the speed from city Y back to city X is 60 km/h (let's call this y).
  • Step 2: Use the formula for average speed when traveling two different speeds. The formula is Average speed = 2xy / (x + y).
  • Step 3: Substitute the values of x and y into the formula. Here, x = 80 and y = 60.
  • Step 4: Calculate the numerator: 2 * 80 * 60. This equals 9600.
  • Step 5: Calculate the denominator: 80 + 60. This equals 140.
  • Step 6: Divide the numerator by the denominator: 9600 / 140. This equals 68.57.
  • Step 7: Round the result to a reasonable number of decimal places if necessary. The average speed for the entire journey is approximately 72 km/h.
  • Average Speed Calculation – The average speed for a round trip is calculated using the formula 2xy / (x + y), where x and y are the speeds in each direction.
  • Harmonic Mean – The average speed in this scenario is a specific case of the harmonic mean, which is used when dealing with rates.
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