SOLUTION: A six passenger plan cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amout of times as it flies 5 miles against the wind, then what is the wind

Question 197828: A six passenger plan cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amout of times as it flies 5 miles against the wind, then what is the wind speed?
I am looking for the formula or the way to arrange the equation. I think it might be D=r/t but I'm not sure. I'll solve once I know the formula or how to arrange the equation.
Thanks so much!!
Amber
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let w = speed of the wind (in miles per hour)

Note: if a plane's speed in still air is 180 mph, then the speed with the wind "w" is 180+w (since going with the wind speeds up the plane) and the speed against the wind is 180-w (since going against the wind slows the plane down)

Start with the distance-rate-time formula

Plug in and (see above)

Divide both sides by 180+w.

Rearrange the equation

-------------------------

Go back to the distance-rate-time formula

Plug in and (see note above)

Since the times are equal, this means that we can plug in

Multiply both sides by 180+w.

Rearrange the terms.

Distribute.

Subtract from both sides.

Add to both sides.

Combine like terms on the left side.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

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Answer:

So the solution is which means that the speed of the wind is 30 mph.
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