SOLUTION: how do i set up a problem like this, i remeber my teacher showing me how to draw some kind of chart, but i don't remeber it. A plane leaves Chicago and heads for Columbus, which

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: how do i set up a problem like this, i remeber my teacher showing me how to draw some kind of chart, but i don't remeber it. A plane leaves Chicago and heads for Columbus, which      Log On

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Question 176889: how do i set up a problem like this, i remeber my teacher showing me how to draw some kind of chart, but i don't remeber it.
A plane leaves Chicago and heads for Columbus, which is 300 miles away. The plane, flying with the wind, takes 40 minutes. The plane returns to chicago, traveling against the wind, in 45 minutes. Find the rate of the wind and the rate of the plane with no wind
thanks

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let w= the wind speed in mi/hr
Let p= the speed of the plane in still air in mi/hr
With the wind:
(1) 300+=+%28p+%2B+w%29%2A%2840%2F60%29
(2) 300+=+%28p+-+w%29%2A%2845%2F60%29
Set the right sides equal to eachother
%28p+%2B+w%29%2A%2840%2F60%29+=+%28p+-+w%29%2A%2845%2F60%29
Multiply both sides by 60
40p+%2B+40w+=+45p+-+45w
Divide both sides by 5
8p+%2B+8w+=+9p+-+9w
p+=+17w
Substitute this back in (1)
(1) 300+=+%28p+%2B+w%29%2A%2840%2F60%29
300+=+%2817w+%2B+w%29%2A%282%2F3%29
Multiply both sides by 3%2F2
450+=+18w
w+=+25 mi/hr
and, since
p+=+17w
p+=+425 mi/hr
The speed of the plane in still air is 425 mi/hr
The speed of the wind is 25 mi/hr
check:
(1) 300+=+%28p+%2B+w%29%2A%2840%2F60%29
(1) 300+=+450%2A%2840%2F60%29
450+=+450
OK