A plane maintains an average speed of 225mph from London to New York. It then returns from New York to London at an average speed of 180mph. What is the average speed for the entire journey?
Hint: It doesn't matter what the distance is, so you can try using 3,600 miles.
It doesn't matter what the actual distance is from London to New York, so for the solution it's easiest to use 3,600 miles, also Time = Distance ÷ Speed:
The outward journey took 3600 ÷ 225 = 16 hours.
The return journey took 3600 ÷ 180 = 20 hours.
Therefore the total time was 36 hours, over a total distance of 7,200 miles. Using Speed = Distance ÷ Time we can see that the average speed is 7200 / 36 = 200 mph. QED.
To show that it doesn't matter what distance we use, we can call the distance D. We then have the outward journey taking D ÷ 225, and the return journey taking D ÷ 180. So the average speed is 2D / (D ÷ 225 + D ÷ 180). Tbe D will cancel and simplification will leave the answer as 81000 ÷ 405 = 200 mph, as required.