SOLUTION: - I am confused how to work this problem. An airplane can fly downwind a distance of 800 miles in 1.6 hours. The return trip against the same wind takes 2 hours. Find the speed

Algebra ->  Test -> SOLUTION: - I am confused how to work this problem. An airplane can fly downwind a distance of 800 miles in 1.6 hours. The return trip against the same wind takes 2 hours. Find the speed      Log On


   

Question 870939: -
I am confused how to work this problem.
An airplane can fly downwind a distance of 800 miles in 1.6 hours. The return trip against the same wind takes 2 hours. Find the speed of the wind.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the plane in still air
Let +w+ = the speed of the wind
--------------------------------
Flying down wind:
(1) +800+=+%28+s+%2B+w+%29%2A1.6+
Flying upwind:
(2) +800+=+%28+s+-+w+%29%2A2+
-----------------------
(1) +1.6s+%2B+1.6w+=+800+
(1) +16s+%2B+16w+=+8000+
and
(2) +2s+-+2w+=+800+
-----------------------
Multiply both sides of (2) by +8+
and subtract (2) from (1)
(1) +16s+%2B+16w+=+8000+
(2) +-16s+%2B+16w+=+-6400+
+32w+=+1600+
+w+=+50+
The windspeed is 50 mi/hr
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check:
(2) +800+=+%28+s+-+w+%29%2A2+
(2) +800+=+%28+s+-+50+%29%2A2+
(2) +800+=+2s+-+100+
(2) +2s+=+900+
(2) +s+=+450+
and
(1) +800+=+%28+s+%2B+w+%29%2A1.6+
(1) +800+=+%28+450+%2B+50+%29%2A1.6+
(1) +800+=+500%2A1.6+
(1) +800+=+800+
OK