SOLUTION: A plain travels 560 miles to San Francisco and back. The trip there was with the wind. It took 7 hours. The trip back was into the wind. The trip back took 14 hours. Find the speed

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Question 175912: A plain travels 560 miles to San Francisco and back. The trip there was with the wind. It took 7 hours. The trip back was into the wind. The trip back took 14 hours. Find the speed of the plain in still air and the speed of the wind.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let p= speed of plane in still air
Let w= speed of the wind
with the wind:
(1) d+=+%28p+%2B+w%29%2At%5B1%5D
Against the wind:
(2) d+=+%28p+-+w%29%2At%5B2%5D
given:
t%5B1%5D+=+7hrs
t%5B2%5D+=+14hrs
d+=+560mi
rewriting (1) and (2),
(1) 560+=+%28p+%2B+w%29%2A7
(2) 560+=+%28p+-+w%29%2A14
------------------------
(1) 7p+%2B+7w+=+560
(2) 14p+-+14w+=+560
Multiply (1) by 2 and add to (2)
(1) 14p+%2B+14w+=+1120
(2) 14p+-+14w+=+560
28p+=+1680
p+=+60 mi/hr
(1) 560+=+%2860+%2B+w%29%2A7
560+=+420+%2B+7w
7w+=+140
w+=+20mi/hr
The plane's speed in still air was 60 mi/hr
the wind speed was 20 mi/hr