Question 876953
Let {{{ w }}} = the windspeed in mi/hr
{{{ 600 + w }}} = the speed of the plane
flying with the wind
{{{ 600 - w }}} = the speed if the wind 
flying against the wind
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(1) {{{ 1449 = ( 600 - w )*t[1] }}}
(2) {{{ 1539 = ( 600 + w )*t[2] }}}
(3) {{{ t[1] + t[2] = 5 }}}
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There are 3 equations and 3 unknowns
so it's solvable
(1) {{{ t[1] = 1449 / ( 600 - w ) }}}
(2) {{{ t[2] = 1539 / ( 600 + w ) }}}
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By substitution:
(3) {{{ 1449 / ( 600 - w )  + 1539 / ( 600 + w ) = 5 }}}
Multiply both sides by {{{ ( 600 - w )*( 600 + w ) }}}
(3) {{{ 1449*( 600 + w ) + 1539*( 600 - w ) = 5*( 360000 - w^2 ) }}}
(3) {{{ 869400 + 1449w + 923400 - 1539w = 1800000 - 5w^2 }}}
(3) {{{ 5w^2 + 2988w + 1792800 - 1800000 = 0 }}}
(3) {{{ 5w^2 - 90w - 7200 = 0 }}}
(3) {{{ w^2 - 18w - 1440 = 0 }}}
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I'll try completing the square:
(3) {{{ w^2 - 18w + ( 18/2 )^2 = 1440 + ( 18/2 )^2 }}}
(3) {{{ w^2 - 18w + 81 = 1440 + 81 }}}
(3) {{{ ( w - 9 )^2 = 1521 }}}
(3) {{{ ( w - 9 )^2 = 39^2 }}}
Take the square root of both sides
(3) {{{ w - 9 = 39 }}}
(3) {{{ w = 48 }}}
The windspeed is 48 mi/hr
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check:
(1) {{{ 1449 = ( 600 - 48 )*t[1] }}}
(1) {{{ t[1] = 1449 / 552 }}}
(1) {{{ t[1] = 2.625 }}}
and
(2) {{{ t[2] = 1539 / ( 600 + 48 ) }}}
(2) {{{ t[2] = 1539 / 648 }}}
(2) {{{ t[2] = 2.375 }}}
and
(3) {{{ t[1] + t[2] = 5 }}}
(3) {{{ 2.625 + 2.375 = 5 }}}
(3) {{{ 5 = 5 }}}
OK