Question 1094426
Let {{{ s }}} = the speed of the plane in still air
Let {{{ w }}} = the wind speed
{{{ 36/60 = .6 }}} ( minutes to hrs )
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Flying against the wind:
(1) {{{ 1400 = ( s - w )*4.6 }}}
Flying with the wind:
(2) {{{ 1400 = ( s + w )*4 }}}
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(2) {{{ 1400 = 4s + 4w }}}
(2) {{{ 4s = 1400 - 4w }}}
(2) {{{ s = 350 - w }}}
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Plug (2) into (1)
(1) {{{ 1400 = ( 350 - w - w )*4.6 }}}
(1) {{{ 1400 = ( 350 - 2w )*4.6 }}}
(1) {{{ 1400 = 1610 - 9.2w }}}
(1) {{{ 9.2w = 1610 - 1400 }}}
(1) {{{ 9.2w = 210 }}}
(1) {{{ w = 22.826 }}}
and
(2) {{{ s = 350 - 22.826 }}}
(2) {{{ s = 327.174 }}}
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The speed of the plane in still air is 327.174 mi/hr
The wind speed is 22.826 mi/hr
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check:
(1) {{{ 1400 = ( s-w )*4.6 }}}
(1) {{{ 1400 = ( 327.174 - 22.826 )*4.6 }}}
(1) {{{ 1400 = 304.348*4.6 }}}
(1) {{{ 1400 = 1400.0008 }}}
close enough
(2) {{{ 1400 = ( s+w )*4 }}}
(2) {{{ 1400 = ( 327.174 + 22.826 )*4 }}}
(2) {{{ 1400 = 350*4 }}}
(2) {{{ 1400 = 1400 }}}
OK
Get a 2nd opinion if needed