SOLUTION: Boy do I need help! Here's the problem: An airplane can fly downwind a distance of 600miles in 2hrs. However, the return trip against the same wind takes three hours. Find the spee

Question 31886This question is from textbook Beginning and Intermediate Algebra
: Boy do I need help! Here's the problem: An airplane can fly downwind a distance of 600miles in 2hrs. However, the return trip against the same wind takes three hours. Find the speed of the wind.
I tried to make a chart and ended up that the wind was going 250 miles an hour and I don't think that sounds right. Any help would be really appreciated. Thank you,Liz This question is from textbook Beginning and Intermediate Algebra

Answer by mbarugel(146) (Show Source): You can put this solution on YOUR website!
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:

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:

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

And then replace this X into the first equation:

So the speed of the wind is 50 mph.

I hope this helps!
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