SOLUTION: 1.A plane travels from Orlando to Denver and back again. On the five-hour trip from Orlando to Denver, the plane has a tailwind of 40 miles per hour. On the return trip from Denve

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: 1.A plane travels from Orlando to Denver and back again. On the five-hour trip from Orlando to Denver, the plane has a tailwind of 40 miles per hour. On the return trip from Denve      Log On

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Question 633370: 1.A plane travels from Orlando to Denver and back again. On the five-hour trip from Orlando to Denver, the plane has a tailwind of 40 miles per hour. On the return trip from Denver to Orlando, the plane faces a headwind of 40 miles per hour. This trip takes six hours. What is the speed of the airplane in still air?
please show work
Answer by josmiceli(9817) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = the speed of the plane in still air
+p+%2B+40+ = speed of plane from Orlando to Denver in mi/hr
+p+-+40+ = speed of plane from Denver to Orlando in mi/hr
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1st trip:
+d+=+%28+p+%2B+40+%29%2A5+
2nd trip:
+d+=+%28+p+-+40+%29%2A6+
----------------
By substitution:
+%28p+%2B+40+%29%2A5+=+%28+p+-+40+%29%2A6+
+5p+%2B+200+=+6p+-+240+
+p+=+440+
440 mi/hr is the speed of the plane in still air
check:
+d+=+%28+440+%2B+40+%29%2A5+
+d+=+480%2A5+
+d+=+2400+ mi
and
+2400+=+%28+p+-+40+%29%2A6+
+2400+=+6p+-+240+
+6p+=+2640+
+p+=+440+ mi/hr
OK