Question 862980
Let {{{ s }}} = the speed of the plane in still air
Let {{{ w }}} = the speed of the wind
{{{ s - w }}} = the speed of the plane against the wind
{{{ s + w }}} = the speed of the plane with the wind 
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Against the wind:
(1) {{{ 600 = ( s - w )*2 }}}
With the wind:
(2) {{{ 600 = ( s + w )*( 5/3 ) }}}
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(1) {{{ 2s - 2w = 600 }}}
(1) {{{ s - w = 300 }}}
and
(2) {{{ 1800 = 5s + 5w }}}
(2) {{{ s + w = 360 }}}
Add the equations
(1) {{{ s - w = 300 }}}
(2) {{{ s + w = 360 }}}
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{{{ 2s = 660 }}}
{{{ s = 330 }}}
The speed of the plane in still air is 330 km/hr
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check:
(1) {{{ 600 = ( 330 - w )*2 }}}
(1) {{{ 600 = 660 - 2w }}}
(1) {{{ 2w = 60 }}}
(1) {{{ w = 30 }}} 
and
(2) {{{ 600 = ( 330 + w )*( 5/3 ) }}}
(2) {{{ 1800 = 1650 + 5w }}}
(2) {{{ 5w = 150 }}}
(2) {{{ w = 30 }}}
OK