SOLUTION: A plane traveled 756 miles to Shanghai and back. the trip was with wind. it took 9 hours. the trip back was into the air. the trip back took 18 hours. find the speed of the plane i

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Question 414660: A plane traveled 756 miles to Shanghai and back. the trip was with wind. it took 9 hours. the trip back was into the air. the trip back took 18 hours. find the speed of the plane in still air and the speed of the wind.
so far..i divided 756/9 = 84 (wind) and i divided 756/18 = 42(air)
but i don't know how to set the equation up.
if you could that would be great! :)
Found 2 solutions by josmiceli, sudhanshu_kmr:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You have 2 trips, each one is 756 mi.
Let s = the speed of the plane in still air
Let w = the wind speed
Speed with the wind = s+%2B+w
Speed against the wind = s+-+w
d+=+756 mi
----------------------
given:
With the wind:
(1) 756+=+%28s+%2B+w%29%2A9
against the wind:
(2) 756+=+%28s+-+w%29%2A18
-----------------
(1) 756+=+%28s+%2B+w%29%2A9
(1) 84+=+s+%2B+w+
and
(2) 756+=+%28s+-+w%29%2A18
(2) 42+=+s+-+w+
----------------
Add equations (1) and (2)
126+=+2s
s+=+63
and
(2) 42+=+s+-+w+
(2) 42+=+63+-+w+
(2) w+=+63+-+42
w+=+21
The speed of the plane in still air is 63 mi/hr
The wind speed is 21 mi/hr
check answers:
(1) 756+=+%28s+%2B+w%29%2A9
(1) 756+=+%2863+%2B+21%29%2A9
(1) 756+=+84%2A9
(1) 756+=+756
and
(2) 756+=+%28s+-+w%29%2A18
(2) 756+=+%2863+-+21%29%2A18
(2) 756+=+42%2A18
(2) 756++=+756
OK
In practical terms, I don't think an airplane could
stay in the air doing only 63 mi/hr, but I think my method is good.

Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!

speed of the plane in still air = x mph, speed of the wind = y mph
speed the the plane with wind i.e x + y = 756/9 = 84

speed of the plane against the wind i.e x-y = 756/18 = 42

now, after adding these equations,..
2x = 126
=> x = 63
y = 84-63 = 21

so speed of plane in still air = 63 mph
speed of the wind = 21 mph