Solution: Getting There and Back Math Puzzle

Many people immediately answer that the flying time is the same. What you lose because of a headwind in one direction should be the same as what you gain owing to a tailwind on the return trip. But if you do the calculations, you'll see that this isn't the case.

With no wind, the round trip will take 4 hours: 1,600 km (1,000 mi) at 800 km/h (500 mph) means the trip is 2 hours each way.

With a 200 km/h headwind, the ground speed is 600 km/h. The time it takes to cover 1,600 km is

 

1,600 km / 600 km/h ( 370 mph) = 2.67 hours, or 2 hours and 40 minutes

 

In the other direction the ground speed is 1,000 km/h (620 mph) so the time it takes to go 1,600 km is

 

1,600 km / 1,000 km/h = 1.6 hours, or 1 hour and 36 minutes

 

The total travel time is 4 hours and 16 minutes.

Let's say that the wind speed is increased to 400 km/h (250 mph). Then the ground speed with a tailwind is 1,200 km/h (750 mph), and the travel time in that direction is

 

1,600 km / 1,200 km/h = 1.33 hours, or 1 hour and 20 minutes

 

In the other direction the ground speed is 400 km/h so the travel time is

 

1,600 km / 400 km/h = 4 hours.

 

The total travel time is 5 hours and 20 minutes. This is an hour longer than with the wind at 200 km/h.

Try the calculation with different wind speeds and see what your results are.  What would happen to the total time for the trip if the wind speed were 800 km/h?