SOLUTION: With a wind velocity of 30 miles per hour, it takes an airplane as long to travel 840 miles with the wind as 660 miles against it. how fast can the airplane travel in still air?

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Question 653157: With a wind velocity of 30 miles per hour, it takes an airplane as long to travel 840 miles with the wind as 660 miles against it. how fast can the airplane travel in still air?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = speed of plane in still air
+p+%2B+30+ = speed of plane flying with the wind
+p+-+30+ = speed of plane flying against the wind
Let +t+ = flight time in both directions
---------------
Flying with the wind:
(1) +840+=+%28+p+%2B+30+%29%2At+
Flying against the wind:
(2) +660+=+%28+p+-+30+%29%2At+
----------------------
(1) +t+=+840+%2F+%28+p+%2B+30+%29+
(2) +t+=+660+%2F+%28+p+-+30+%29+
By substitution:
+840+%2F+%28+p+%2B+30+%29+=+660+%2F+%28+p+-+30+%29+
Multiply both sides by +%28+p+%2B+30+%29%2A%28+p+-+30+%29+
+840%2A%28+p+-+30+%29+=+660%2A%28+p+%2B+30+%29+
+840p+-+25200+=+660p+%2B+19800+
+180p+=+45000+
+p+=+250+
The speed of the plane in still air is 250 mi/hr
check:
(1) +t+=+840+%2F+%28+250+%2B+30+%29+
(1) +t+=+840+%2F+280+
(1) +t+=+3+ hrs
and
(2) +t+=+660+%2F+%28+250+-+30+%29+
(2) +t+=+660+%2F+220+
(2) +t+=+3+ hrs
OK