   SEARCH HOME Math Central Quandaries & Queries  Question from Shelby, a student: An Airplane flies a certain distance in 3 hours going WITH a 40km/hr wind. It travels the same distance in 5 hours when going against the wind. What is it's speed and how long would it take to travel the same distance in still air? Distance = speed x time Hi Selby,

There are two keys to solving this problem. One is your final statement "Distance = speed x time". The second is that if you are flying with the wind then your speed increases by the speed of the wind and if you are flying against the wind then your speed decreases by the speed of the wind. Thus for example if your speed in still air is 100 km/hr then your speed with the wind is 100 + 40 = 140 km/hr and your speed against the wind is 100 - 40 = 60 km/hr.

But you don't know the speed in still air so suppose it's s km/hr.

What is you speed with the wind? Use distance = speed x time to find how far you travel in 3 hours.

What is you speed against the wind? Use distance = speed x time to find how far you travel in 5 hours.

These two distances are the same. Solve for s.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.