Question 825285
Let {{{ w }}} = the speed of the wind
Flying with the wind
Let {{{ t }}} = the flying time flying with the wind
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with the wind
(1) {{{ 990 = ( 600 + w )*t }}}
against the wind
(2) {{{ 990 = ( 600 - w )*( 10/3 - t ) }}}
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(1) {{{ t = 990 / ( 600 + w ) }}}
(2) {{{ 990 = 2000 - (10/3)*w - 600t + w*t }}}
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Substitute (1) into (2)
(2) {{{ 990 = 2000 - (10/3)*w - ( 600 - w )*( 990/( 600 + w )) }}}
(2) {{{ -1010 = - (10/3)*w - ( 600 - w )*( 990/( 600 + w )) }}}
(2) {{{ 1010 =  (10/3)*w + ( 600 - w )*( 990/( 600 + w )) }}}
Multiply both sides by {{{ 3*( 600 + w ) }}}
(2) {{{ 3030*( 600 + w ) = 10w*( 600 + w ) + 3*990*( 600 - w ) }}}
(2) {{{ 1818000 + 3030w  = 6000w + 10w^2 + 1782000 - 2970w  }}}
(2) {{{ 10w^2 - 3030w + 6000w - 2970w + 1782000 - 1818000 = 0 }}}
(2) {{{ 10w^2 - 36000 = 0 }}}
(2) {{{ 10w^2 = 36000 }}}
(2) {{{ w^2 = 3600 }}}
(2) {{{ w = 60 }}}
The wind speed is 60 km/hr
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check:
(1) {{{ 990 = ( 600 + 60 )*t }}}
(1) {{{ t = 990 / 660 }}}
(1) {{{ t = 1.5 }}} hrs
and
(2) {{{ 990 = ( 600 - 60 )*( 10/3 - t ) }}}
(2) {{{ 990 = 540*( 10/3 - t ) }}}
(2) {{{ 990 = 1800 - 540t }}}
(2) {{{ 540t = 1800 - 990 }}}
(2) {{{ 540t = 810 }}}
(2) {{{ t = 1.5 }}} hrs
OK