Question 507609
Let {{{s}}} = the Pilot's speed in still air
Let {{{w}}} = the wind speed
Let {{{t}}} = The pilot's time flying with and against the wind
given:
{{{ s + w }}} = speed flying with the wind
{{{ s - w }}} = speed flying against the wind
{{{ s = 230 }}}
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With the wind:
(1) {{{ 400 = ( 230 + w )*t }}}
Against the wind:
(2) {{{ 336 = ( 230 - w )*t }}}
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(1) {{{ 400 = 230t + wt }}}
(2) {{{ 336 = 230t - wt }}}
Add the equations
{{{ 736 = 460t }}}
{{{ t = 736/460 }}}
{{{ t = 1.6 }}} hrs
Plug this back into (1) or (2)
(1) {{{ 400 = 230*1.6 + w*1.6 }}}
(1) {{{ 400 = 368 + 1.6w }}}
(1) {{{ 1.6w = 32 }}}
(1) {{{ w = 20 }}}
The wind speed is 20 mi/hr
check answer:
(2) {{{ 336 = ( 230 - 20 )*1.6 }}}
(2) {{{ 336 = 210*1.6 }}}
(2) {{{ 336 = 336 }}}
OK