Question 1058973
Let {{{ s }}} = the speed of the plane in km/hr in still air
{{{ s + 10 }}} = the speed of the plane flying with the wind
{{{ s - 10 }}} = the speed of the plane flying against the wind
Let {{{ t }}} = time in hrs flying with the wind
The one-way distance is {{{ 300/2 = 150 }}} km
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Equation for flying with the wind:
(1) {{{ 150 = ( s + 10 )*t }}}
Equation for flying against the wind:
(2) {{{ 150 = ( s - 10 )*( 4.5 - t ) }}}
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(1) {{{ t = 150/( s + 10 ) }}}
and
(2) {{{ 150 = 4.5s - 45 - s*t + 10t }}}
(2) {{{ 150 + 45 = 4.5s - t*( s - 10 ) }}}
Plug (1) into (2)
(2) {{{ 150 + 45 = 4.5s - ( 150/( s+10 ) )*( s - 10 ) }}}
(2) {{{ 195 = 4.5s -( 150s / ( s+10 ) - 1500/( s + 10 )) }}|}
(2) {{{ 195 = 4.5s - 150s / ( s+10 ) + 1500/( s + 10 ) }}|}
Multiply both sides by {{{ s + 10 }}}
(2) {{{ 195*( s+ 10 ) = 4.5s*( s + 10 ) - 150s + 1500 }}}
(2) {{{ 195s + 1950 = 4.5s^2 + 45s - 150s + 1500 }}}
(2) {{{ 4.5s^2 - 195s + 45s - 150s + 1500 - 1950 = 0 }}}
(2) {{{ 4.5s^2 -300s - 450 = 0 }}}
(2) {{{ 45s^2 - 3000s - 4500 = 0 }}}
(2) {{{ 9s^2 - 600s - 900 = 0 }}}
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Use quadratic formula
{{{ s = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 9 }}}
{{{ b = -600 }}}
{{{ c = -900 }}}
{{{ s = (-(-600) +- sqrt( (-600)^2 - 4*9*(-900) )) / (2*9) }}}
{{{ s = ( 600 +- sqrt( 360000 + 32400 )) / 18 }}}
{{{ s = ( 600 +- sqrt( 392400 )  ) / 18 }}}
{{{ s = ( 600 + 626.418 ) / 18 }}}
{{{ s = 1226.418/18 }}}
{{{ s = 68.134 }}} 
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The speed of the plane in still air is 68.134 km/hr
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check:
(1) {{{ 150 = ( s + 10 )*t }}}
(1) {{{ 150 = ( 68.134 + 10 )*t}}}
(1) {{{ t = 150 / 78.134 }}}
(1) {{{ t = 1.92 }}} hrs
and
(2) {{{ 150 = ( s - 10 )*( 4.5 - t ) }}}
(2) {{{ 150 = ( 68.134 - 10 )*( 4.5 - t ) }}}
(2) {{{ 150 / 58.134 = 4.5 - t }}}
(2) {{{ 2.5802 = 4.5 - t }}}
(2) {{{ t = 4.5 - 2.5802 }}}
(2) {{{ t = 1.92 }}} hrs
OK
Pretty strange numbers -ususally they
come out simple decimals. You might
want a 2nd opinion, too.