An airplane flies 560 miles with a tail wind in 2 hr 20 minutes. It takes 3 hour

Question

An airplane flies 560 miles with a tail wind in 2 hr 20 minutes.  It takes 3 hours to fly against the head wind.  Find the speed of the airplane in still air and the speed of the wind.  

Explanation / Answer

    a = the speed of the airplane instill air, measured in miles per hour     w = the speed of the wind, measuredin miles per hour     2 hr, 20 min = 7 / 3 hr When the airplane is flying with a tail wind, the its speedrelative to the ground is:     speed1 = a + w and the flight takes 7 / 3 hours     ( a + w ) mph   *    ( 7 / 3 ) hr   =    560 mi    =>     ( 7 / 3 )a    +   ( 7 / 3 )w    =    560 When the airplane is flying against a head wind, its speed relativeto the ground is:     speed2 = a - w and the flight takes 3 hours:     ( a - w ) mph   *    ( 3 ) hr    =   560 mi    =>     3a    -   3w    =    560 Solve the system:     ( 7 / 3 )a    +   ( 7 / 3 )w    =    560     3a    -   3w    =    560 (1)     3a    -   3w    =    560   =>     3a    =   3w + 560    =>     a    =   w    +    560 / 3 (2)     ( 7 / 3 )a    +   ( 7 / 3 )w    =   560    =>     ( 7 / 3 )( w   +    560 / 3 )   +    ( 7 / 3 )w   =    560    =>     ( 7 / 3 )w    +   3920 / 9    +    ( 7 / 3)w    =    560   =>     ( 14 / 3 )w   =    560   -    3920 / 9   =>     ( 14 / 3 )w   =    5040/ 9    -    3920 / 9   =>     ( 14 / 3 )w   =    1120/ 9    =>     w    =    ( 3 / 14 )( 1120 / 9 )   =    3360 / 126   =    80 / 3 mph =>     a    =    80 / 3   +    560 / 3   =    640 / 3 mph

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