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Puzzle Details

A plane maintains an average speed of 696mph from London to New York.

It then returns from New York to London at an average speed of 145mph.

What is the average speed for the entire journey?

Note that we cannon add the speeds together to find the average, so 420.5 mph isn't correct.

If we let the distance be x miles.

Using Time = Distance ÷ Speed:

x                        x
Outward trip = --- hours. Return trip = --- hours.
696                      145

The total distance travelled is 2x.

x     x
Total time = --- + --- hours.
696   145

Since Speed = Distance ÷ Time, the average speed is:

2x
--------
x     x
--- + ---
696   145

The x's cancel to give

2
--------
1     1
--- + ---
696   145

2
-------
1 ÷ 120

This simplifies to give 240 mph. QED.

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