### Brain Teasers

# Flying Around

Assume a red plane leaves from city A to city B and at the same time a blue plane from city B heads toward city A. The wind current is around 5 mph and is traveling against the Blue plane. Both planes are travelling at 120 miles per hour relative to the wind (not the ground). If the distance between the two cities is 300 miles, after how long will the two planes meet?

### Answer

Set up 2 equations:distance = rate * time

speed going with the wind = 120 + 5

speed against the wind = 120 - 5

d = (120+5)t

300 - d = (120-5)t

Add the two equations together:

300 = 125t + 115t

300 = 240t

1.25 = t

They will meet in 1.25 hrs.

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## Comments

A ok for the math. However, the problem has two unrealistic assumptions. First, that wind direction and speed are constant over the distance point A to B and point B to A. Second, that flight paths from A to B and from B to A are the same. It is never the same.

can you please explain yourself a little more? What do you mean flight paths are never the same? I never flew in a plane b4, maybe thats why.

The flight paths can be similar enough so that the differences are negligible. However, the wind speed is not important, because both planes are traveling at the same speed relative to the wind. Of course, we're assuming the same wind over a 300 mile span, which is a bit of a stretch. But in teasers, some assumptions usually have to be made that might not be too realistic.

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