SOLUTION: An airplane took 2 hours to fly 600 km against a head wind. The return trip with the wind took 1 2/3. Fine the speed of the plane in still air. Thank YOU.

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Question 862980: An airplane took 2 hours to fly 600 km against a head wind. The return trip with the wind took 1 2/3. Fine the speed of the plane in still air.
Thank YOU.
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
+s+-+w+ = the speed of the plane against the wind
+s+%2B+w+ = the speed of the plane with the wind
--------------------------------------------
Against the wind:
(1) +600+=+%28+s+-+w+%29%2A2+
With the wind:
(2) +600+=+%28+s+%2B+w+%29%2A%28+5%2F3+%29+
----------------------------
(1) +2s+-+2w+=+600+
(1) +s+-+w+=+300+
and
(2) +1800+=+5s+%2B+5w+
(2) +s+%2B+w+=+360+
Add the equations
(1) +s+-+w+=+300+
(2) +s+%2B+w+=+360+
-------------------
+2s+=+660+
+s+=+330+
The speed of the plane in still air is 330 km/hr
-----------------
check:
(1) +600+=+%28+330+-+w+%29%2A2+
(1) +600+=+660+-+2w+
(1) +2w+=+60+
(1) +w+=+30+
and
(2) +600+=+%28+330+%2B+w+%29%2A%28+5%2F3+%29+
(2) +1800+=+1650+%2B+5w+
(2) +5w+=+150+
(2) +w+=+30+
OK