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Find the speed of the plane

A plan flies 420 miles with the wind and 350 miles against the wind in the same length of time . If the speed is 15mph, find the speed of the plane still in the air.  

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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
Check Marked as Best Answer
Let x be the speed of the plane in the still air, and w be the wind speed.
Balance by the time,
420/(x+w) = 350/(x-w)
Cross multiplication after canceling 70 gives,
6(x-w) = 5(x+w)
=> x = 11w = 11*15 = 165 mph <==Answer
Attn: Here I assumed w = 15 mph.
Brad M. | STEM Specialist plus Business, Accounting, Investment & EditingSTEM Specialist plus Business, Accountin...
4.9 4.9 (233 lesson ratings) (233)
Hi T -- since the wind makes a 70 mile difference, the wind hinders the 350mi leg by 35mi ... "still air" trip would be 385mi => the equivalent of 11 "winds" ...
"still air" mph = 11 "wind" mph ==> 165mph ...  Regards, ma'am :)