Question 1007320
Let {{{ s }}} = his speed with no wind
{{{ s + 6 }}} = his speed riding with the wind
{{{ s - 6 }}} = his speed riding into the wind
Let {{{ t }}} = his time in hrs riding both ways
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Riding with the wind:
(1) {{{ 15 = ( s + 6 )*t }}}
Riding against the wind:
(2) {{{ 9 = ( s - 6 )*t }}}
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(1) {{{ t = 15/( s + 6 ) }}}
Substitute this result into (2)
(2) {{{ 9 = ( s - 6 )*( 15/( s + 6 )) }}}
Multiply both sides by {{{ s + 6 }}}
(2) {{{ 9*( s + 6 ) = 15*( s - 6 ) }}}
(2) {{{ 9s + 54 = 15s - 90 }}}
(2) {{{ 6s = 144 }}}
(2) {{{ s = 24 }}}
His speed with no wind is 24 mi/hr
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check:
(1) {{{ 15 = ( s + 6 )*t }}}
(1) {{{ 15 = ( 24 + 6 )*t }}}
(1) {{{ 15 = 30t }}}
(1) {{{ t = 1/2 }}}
and
(2) {{{ 9 = ( s - 6 )*t }}}
(2) {{{ 9 = ( 24 - 6 )*t }}}
(2) {{{ 9 = 18t }}}
(2) {{{ t = 1/2 }}}
OK