SOLUTION: Against the winda commercial airline in south America flew 390 miles in 3 hours. with a tailwind the return trip took 2.5 hours. what was the speed of the plane in still air, what

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Question 934938: Against the winda commercial airline in south America flew 390 miles in 3 hours. with a tailwind the return trip took 2.5 hours. what was the speed of the plane in still air, what was the speed of the wind?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = the speed of the wind
Let +s+ = the speed of the plane in still air
+s+-+w+ = speed of the plane going against the wind
+s+%2B+w+ = speed of the plane going with the wind
------------------------------------------------
(1) +390+=+%28+s+-+w+%29%2A3+
(2) +390+=+%28+s+%2B+w+%29%2A2.5+
--------------------------
(1) +390+=+3s+-+3w+
(2) +390+=+2.5s+%2B+2.5w+
--------------------------
Multiply both sides of (1) by +5+
(1) +1950+=+15s+-+15w+
Multiply both sides of (2) by +6+
(2) +2340+=+15s+%2B+15w+
--------------------------
Add the equations
+4290+=+30s+
+s+=+143+
----------------
By substitution:
(1) +390+=+3s+-+3w+
(1) +130+=+s+-+w+
(1) +130+=+143+-+w+
(1) +w+=+13+
---------------
The speed of the wind is 13 mi/hr
The speed of the plane in still air is 143 mi/hr
---------------
check:
(1) +390+=+%28+s+-+w+%29%2A3+
(1) +390+=+%28+143+-+13+%29%2A3+
(1) +390+=+130%2A3+
(1) +390+=+390+
You can check other equation