A train travels from city X to city Y at a speed of 45 km/h and returns at a spe

A train travels from city X to city Y at a speed of 45 km/h and returns at a speed of 60 km/h. What is the average speed for the entire journey?

A train travels from city X to city Y at a speed of 45 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 45 km/h (Speed1) and the speed from city Y back to city X is 60 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 * (45 * 60) / (45 + 60).
Step 4: Calculate the product of the speeds: 45 * 60 = 2700.
Step 5: Calculate the sum of the speeds: 45 + 60 = 105.
Step 6: Substitute these values back into the formula: Average Speed = 2 * 2700 / 105.
Step 7: Calculate 2 * 2700 = 5400.
Step 8: Divide 5400 by 105 to find the average speed: 5400 / 105 = 51.42857 km/h.
Step 9: Round the average speed to two decimal places if needed, but the exact average speed is approximately 51.43 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 over the same distance.