Question 723156
Let {{{ w }}} = the wind speed in mi/hr
{{{ 100 + w }}} = the plane's speed going with the wind in mi/hr
{{{ 100 - w }}} = the plane's speed going against the wind in mi/hr
Let {{{ t }}} = plane's time going against the wind in hrs
{{{ 5 - t }}} = planes time going with the wind in hrs
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Equation going against the wind:
(1) {{{ 240 = ( 100 - w )*t }}}
Equation going with the wind:
(2) {{{ 240 = ( 100 + w )*( 5 - t ) }}}
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(2) {{{ 240 = 500 + 5w - 100t - w*t }}}
(2) {{{ w*t + 100t - 5w = 260 }}}
(2) {{{ t*( 100 + w ) = 260 + 5w }}}
and,
(1) {{{ 240 = ( 100 - w )*t }}}
(1) {{{ t = 240 / ( 100 - w ) }}}
Substitute this result into (2)
(2) {{{  (240 / ( 100 - w )) *( 100 + w ) = 260 + 5w }}}
(2) {{{ 240*( 100 + w ) = ( 260 + 5w )*( 100 - w ) }}}
(2) {{{ 24000 + 240w = 26000 + 500w - 260w - 5w^2 }}}
(2) {{{ 5w^2 = 2000 }}}
(2) {{{ w^2 = 400 }}}
(2) {{{ w = 20 }}}
The wind speed is 20 mi/hr
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check answer:
(1) {{{ 240 = ( 100 - w )*t }}}
(1) {{{ 240 = ( 100 - 20 )*t }}}
(1) {{{ 240 = 80t }}}
(1) {{{ t = 3 }}} hrs
and
(2) {{{ 240 = ( 100 + w )*( 5 - t ) }}}
(2) {{{ 240 = ( 100 + 20 )*( 5 - t ) }}}
(2) {{{ 240 / 120 = 5 - t }}}
(2) {{{ 2 = 5 - t }}}
(2) {{{ t = 3 }}} hrs
OK