SOLUTION: Flying with the wind, a plane traveled 510 miles in 3 hours. Flying against the wind, the plane traveled the same distance in 5 hours. Find the rate of the plane in calm air and th

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Question 743918: Flying with the wind, a plane traveled 510 miles in 3 hours. Flying against the wind, the plane traveled the same distance in 5 hours. Find the rate of the plane in calm air and the rate of the wind.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = the speed of the plane in still air in mi/hr
Let +w+ = the speed of the wind in mi/hr
+p+%2B+w+ = plane's speed flying with the wind in mi/hr
+p+-+w+ = plane's speed flying against the wind in mi/hr
--------------------
Flying with the wind:
(1) +510+=+%28+p+%2B+w+%29%2A3+
Flying against the wind:
(2) +510+=+%28+p+-+w+%29%2A5+
----------------------
(1) +3p+%2B+3w+=+510+
and
(2) +5p+-+5w+=+510+
---------------------
(1) +p+%2B+w+=+170+
(2) +p+-+w+=+102+
Add the equations
+2p+=+272+
+p+=+136+
and
(1) +136+%2B+w+=+170+
(1) +w+=+34+
The rate of the plane in calm air is 136 mi/hr
The rate of the wind is 34 mi/hr
check:
(2) +136+-+34+=+102+
(2) +102+=+102+
OK