Question

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

Answer 1

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