Question 1025505
Let {{{ s }}} = speed of the plane in still air in mi/hr
{{{ s + 30 }}} = the speed of the plane going with the wind
{{{ s - 30 }}} = the speed of the wind going against the wind
Let {{{ t }}} = time in hrs for both trips
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Equation for going against the wind
(1) {{{ 350 = ( s - 30 )*t }}}
Equation for going with the wind:
(2) {{{ 500 = ( s + 30 )*t }}}
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(1) {{{ t = 350 / ( s - 30 ) }}}
Substitute (1) into (2)
(2) {{{ 500 = ( s + 30 )*( 350 / ( s - 30 ) ) }}}
(2) {{{ 500*( s - 30 ) = 350*( s + 30 ) }}}
(2) {{{ 500s - 15000 = 350s + 10500 }}}
(2) {{{ 150s = 25500 }}}
(2) {{{ s = 170 }}}
The speed of the plane in still air is 170 mi/hr
check:
(1) {{{ 350 = ( s - 30 )*t }}}
(1) {{{ 350 = ( 170 - 30 )*t }}}
(1) {{{ 350 = 140t }}}
(1) {{{ t = 2.5 }}}
and
(2) {{{ 500 = ( s + 30 )*t }}}
(2) {{{ 500 = ( 170 + 30 )*t }}}
(2) {{{ 500 = 200t }}}
(2) {{{ t = 2.5 }}}
OK