Question 796955
Let {{{ w }}} = the speed of the wind
Let {{{ s }}} = the speed of the plane in still air
{{{ s + w }}} = the plane's speed going LA to NY
{{{ s - w }}} = the plane's speed going NY to LA
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Flying LA to NY:
(1) {{{ 4000 = ( s + w )*5 }}}
Flying NY to LA:
(2) {{{ 4000  = ( s - w )*6 }}}
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(1) {{{ 4000 = 5s + 5w }}}
(2) {{{ 4000 = 6s - 6w }}}
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Multiply both sides of (1) by {{{ 6 }}}
Multiply both sides of (2) by {{{ 5 }}}
Then add the equations
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(1) {{{ 24000 = 30s + 30w }}}
(2) {{{ 20000 = 30s - 30w }}}
{{{ 44000 = 60s }}}
{{{ s = 733.333 }}} 
and
(1) {{{ 4000 = 5s + 5w }}}
(1) {{{ 800 = s + w }}}
(1) {{{ w = 800 - 733.333 }}}
(1) {{{ w = 66.666 }}}
The speed of the wind is 66.666 mi/hr
The speed of the plane in still air is 733.333 mi/hr
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check:
(1) {{{ 4000 = ( s + w )*5 }}}
(1) {{{ 4000 = ( 733.333 + 66.666 )*5 }}}
(1) {{{ 4000 = 800*5 }}}
(1) {{{ 4000 = 4000 }}}
and
(2) {{{ 4000  = ( s - w )*6 }}}
(2) {{{ 4000  = ( 733.333 - 66.666 )*6 }}}
(2) {{{ 4000 = 666.666*6 }}}
(2) {{{ 4000 = 4000 }}}
OK