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

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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) About Me  (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)


d=rt Start with the distance-rate-time formula


7=%28180%2Bw%29t Plug in d=7 and r=180%2Bw (see above)


7%2F%28180%2Bw%29=t Divide both sides by 180+w.


t=7%2F%28180%2Bw%29 Rearrange the equation


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d=rt Go back to the distance-rate-time formula


5=%28180-w%29t Plug in d=5 and r=180-w (see note above)


5=%28180-w%29%287%2F%28180%2Bw%29%29 Since the times are equal, this means that we can plug in t=7%2F%28180%2Bw%29


5%28180%2Bw%29=%28180-w%297 Multiply both sides by 180+w.


5%28180%2Bw%29=7%28180-w%29 Rearrange the terms.


900%2B5w=1260-7w Distribute.


5w=1260-7w-900 Subtract 900 from both sides.


5w%2B7w=1260-900 Add 7w to both sides.


12w=1260-900 Combine like terms on the left side.


12w=360 Combine like terms on the right side.


w=%28360%29%2F%2812%29 Divide both sides by 12 to isolate w.


w=30 Reduce.


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Answer:

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