Expert: Chanda Walker - 3/20/2009

Question
QUESTION: I can't understand how to set up this problem. What am I missing in setting it up. A six-passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind, then what is the wind speed?

ANSWER: I'll set it up only, because that seems to be what you need but let me know if you still need help.  I'm happy to do that.

note:  the units of mph can be written as m/h
v = 180

5/(v - ws) = time          Unit analysis: m/(m/h)= h
7/(v + ws) = time

5/(v - ws) = 7/(v + ws)

5*(v + ws) = 7*(v- ws)

Hopefully it will be easy from here but if not . . . I'll be around.

---------- FOLLOW-UP ----------

QUESTION: If I worked this correctly, the answer is the wind speed is 180 miles per hour. Is that correct? If not, please show me what I missed.

Answer
Yikes!  That is a lot of wind!  That is the speed of the airplane not the wind I think.

5v + 5ws = 7v - 7ws
12ws = 2v
ws = v/6
ws = 30

I think 30 mph sounds more reasonable.  Did you worked it like this:

5v + 5ws = 7v - 7ws
2ws = 2v  (you subtracted the 7ws across maybe???)
ws = v

Let me know if I can help further.