Question 1079094
Let {{{ w }}} = the speed of the wind in mi/hr
Let {{{ s }}} = the speed of the plane in still air in mi/hr
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Equation for flying with the wind
(1) {{{ 450 = ( s + w )*2 }}}
Equation for flying against the wind
(2) {{{ 450 = ( s - w )*3 }}}
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(1) {{{ 2s + 2w = 450 }}}
(2) {{{ 3s - 3w = 450 }}}
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(1) {{{ s + w = 225 }}}
(2) {{{ s - w = 150 }}}
Add the equations
{{{ 2s = 375 }}}
{{{ s = 187.5 }}}
The speed of the plane in still air is 187.5 mi
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check:
(1) {{{ 450 = ( s + w )*2 }}}
(1) {{{ 450 = ( 187.5 + w )*2 }}}
(1) {{{ 225 = 187.5 + w }}}
(1) {{{ w = 37.5 }}}
and
(2) {{{ 450 = ( s - w )*3 }}}
(2) {{{ 450 = ( 187.5 - w )*3 }}}
(2) {{{ 450 = 562.5 - 3w }}}
(2) {{{ 3w = 112.5 }}}
(2) {{{ w = 37.5 }}}
OK