Question 31886
Hello!
When the airplane flies downwind, the speed of the wind is added to the one of the plane. When it's going against the wind, then it should be subtracted.

Let's call X to the speed of the plane ("without wind") and Y to the speed of the wind. So we get the following equations:

{{{X + Y = 600/2 = 300}}}
When going downwind, the final speed of the plane (plane + wind) is 300 mph, because it travels 600 mph in 2 hours.

The other fact is that when going against the wind takes 3 hours, so its speed is 200 mph (600 miles in 3 hours). So we get the equation:

{{{X - Y = 200}}}

Now let's find Y, which is what we're interested in. Isolate X from the 2nd equation:

{{{X = 200 + Y}}}
And then replace this X into the first equation:
{{{X+ Y=300}}}
{{{200+Y+Y=300}}}
{{{2Y = 300 - 200 = 100}}}
{{{Y = 50}}}

So the speed of the wind is 50 mph.


I hope this helps!
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