SOLUTION: Against the wind a commercial airline in South America flew 360 miles in 3 hours. With a tailwind the return trip took 2.5hours. What was the speed of the plane in still&#

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Question 1098657: Against the wind a commercial airline in South America flew
360
miles in
3 hours. With a tailwind the return trip took
2.5hours. What was the speed of the plane in still​ air? What was the speed of the​ wind?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
             SPEED      TIME    DISTANCE
GOING        r-w         3       360
RETURN       r+w         2.5     360

system%28r-w=360%2F3%2Cr%2Bw=360%2F2.5%29

system%28r-w=120%2Cr%2Bw=144%29-------solve this system.

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 wind speed
---------------------------------
Flying against the wind:
(1) +360+=+%28+s+-+w+%29%2A3+
Flying with the wind:
(2) +360+=+%28+s+%2B+w+%29%2A2.5+
-----------------------------
(1) +3s+-+3w+=+360+
(2) +2.5s+%2B+2.5w+=+360+
Multiply both sides of (1) by +5+
and both sides of (2) by +6+
Then add the equations
------------------------------------
(1) +15s+-+15w+=+1800+
(2) +15s+%2B+15w+=+2160+
------------------------------
+30s+=+3960+
+s+=+132+
and
(1) +360+=+%28+s+-+w+%29%2A3+
(1) +360+=+%28+132+-+w+%29%2A3+
(1) +360+=+396+-+3w+
(1) +3w+=+36+
(1) +w+=+12+
----------------------------
The speed of the plane in still air is 132 mi/hr
The wind speed is 12 mi/hr
-----------------------------
check:
(2) +360+=+%28+s+%2B+w+%29%2A2.5+
(2) +360+=+%28+132+%2B+12+%29%2A2.5+
(2) +360+=+144%2A2.5+
(2) +360+=+360+
OK