Question 1016705
Let {{{ s }}} = the speed of the 
propellor plane in mi/hr
Let {{{ t }}} = time in hrs for the
propellor plane to fly 3,240 mi
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Equation for propellor plane:
(1) {{{ 3240 = s*t }}}
Equation for jet plane:
(2) {{{ 3240 = ( s + 45 )*( t - 1 ) }}}
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(1) {{{ t = 3240/s }}}
(2) {{{ 3240 = s*t + 45t - s - 45 }}}
(2) {{{ 3240 = t*( s + 45 ) - s - 45 }}}
(2) {{{ 3240 = ( 3240/s )*( s + 45 ) - s - 45 }}}
(2) {{{ 3240 = 3240 + 145800/s - s - 45 }}}
(2) {{{ 145800/s = s + 45 }}}
Multiply both sides by {{{ s }}}
(2) {{{ 145800 = s^2 + 45s }}}
(2) {{{ s^2 + 45s - 145800 = 0 }}}
Use quadratic formula
{{{ s = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = 1 }}}
{{{ b = 45 }}}
{{{ c = -145800 
{{{ s = (-45 +- sqrt( 45^2 - 4*1*( -145800 ))/(2*1) }}} 
{{{ s = (-45 +- sqrt( 2025 + 583200 ))/2 }}} 
{{{ s = (-45 +- sqrt( 585225 ))/2 }}} 
{{{ s = ( -45 + 765 ) / 2 }}}
{{{ s = 720/2 }}}
{{{ s = 360 }}}
and
{{{ s + 45 = 405 }}}
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The prop plane flies at 360 mi/hr
The jet plane flies at 405 mi/hr
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check:
(1) {{{ 3240 = s*t }}}
(1) {{{ 3240 = 360t }}}
(1) {{{ t = 9 }}} 
and
(2) {{{ 3240 = ( s + 45 )*( t - 1 ) }}}
(2) {{{ 3240 = 405*( t - 1 ) }}}
(2) {{{ 3240 = 405t - 405 }}}
(2) {{{ 405t = 3645 }}}
(2) {{{ t = 9 }}}
OK