Question 870939
Let {{{ s }}} = the speed of the plane in still air
Let {{{ w }}} = the speed of the wind
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Flying down wind:
(1) {{{ 800 = ( s + w )*1.6 }}}
Flying upwind:
(2) {{{ 800 = ( s - w )*2 }}}
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(1) {{{ 1.6s + 1.6w = 800 }}}
(1) {{{ 16s + 16w = 8000 }}}
and
(2) {{{ 2s - 2w = 800 }}}
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Multiply both sides of (2) by {{{ 8 }}}
and subtract (2) from (1)
(1) {{{ 16s + 16w = 8000 }}}
(2) {{{ -16s + 16w = -6400 }}}
{{{ 32w = 1600 }}}
{{{ w = 50 }}}
The windspeed is 50 mi/hr
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check:
(2) {{{ 800 = ( s - w )*2 }}}
(2) {{{ 800 = ( s - 50 )*2 }}}
(2) {{{ 800 = 2s - 100 }}}
(2) {{{ 2s = 900 }}}
(2) {{{ s = 450 }}}
and
(1) {{{ 800 = ( s + w )*1.6 }}}
(1) {{{ 800 = ( 450 + 50 )*1.6 }}}
(1) {{{ 800 = 500*1.6 }}}
(1) {{{ 800 = 800 }}}
OK