Question 846234
Let {{{ t }}} = his time for running both
with the wind and against the wind
Let {{{ w }}} = the speed of the wind
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With the wind:
(1) {{{ 15 = ( 5 + w )*t }}}
Against the wind:
(2) {{{ 4 = ( 5 - w )*t }}}
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(1) {{{ 15 = 5t + w*t }}}
and
(2) {{{ 4 = 5t - w*t }}}
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Add the equations:
(1) {{{ 15 = 5t + w*t }}}
(2) {{{ 4 = 5t - w*t }}}
{{{ 19 = 10t }}}
{{{ t = 1.9 }}}
and
(2) {{{ 4 = ( 5 - w )*1.9 }}}
(2) {{{ 4 = 9.5 - 1.9w }}}
(2) {{{ 1.9w = 5.5 }}}
(2) {{{ w = 2.895 }}}
check:
(1) {{{ 15 = ( 5 + w )*t }}}
(1) {{{ 15 = ( 5 + 2.895 )*1.9 }}}
(1) {{{ 15 = 7.895*1.9 }}}
(1) {{{ 15 = 15.0005 }}}
and
(2) {{{ 4 = ( 5 - w )*t }}}
(2) {{{ 4 = ( 5 - 2.895 )*1.9 }}}
(2) {{{ 4 = 2.105*1.9 }}}
(2) {{{ 4 = 3.9995 }}}
close enough
The wind speed is 2.895 mi/hr