Question 653157
Let {{{ p }}} = speed of plane in still air
{{{ p + 30 }}} = speed of plane flying with the wind
{{{ p - 30 }}} = speed of plane flying against the wind
Let {{{ t }}} = flight time in both directions
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Flying with the wind:
(1) {{{ 840 = ( p + 30 )*t }}}
Flying against the wind:
(2) {{{ 660 = ( p - 30 )*t }}}
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(1) {{{ t = 840 / ( p + 30 ) }}}
(2) {{{ t = 660 / ( p - 30 ) }}}
By substitution:
{{{ 840 / ( p + 30 ) = 660 / ( p - 30 ) }}}
Multiply both sides by {{{ ( p + 30 )*( p - 30 ) }}}
{{{ 840*( p - 30 ) = 660*( p + 30 ) }}}
{{{ 840p - 25200 = 660p + 19800 }}}
{{{ 180p = 45000 }}}
{{{ p = 250 }}}
The speed of the plane in still air is 250 mi/hr
check:
(1) {{{ t = 840 / ( 250 + 30 ) }}}
(1) {{{ t = 840 / 280 }}}
(1) {{{ t = 3 }}} hrs
and
(2) {{{ t = 660 / ( 250 - 30 ) }}}
(2) {{{ t = 660 / 220 }}}
(2) {{{ t = 3 }}} hrs
OK