Question 739431
The speed of the boat going upstream is
{{{ s - 3 }}} mi/hr
The speed of the boat going downstream is
{{{ s + 3 }}} mi/hr
where {{{ s }}} = the boat's speed in still water
Let {{{ t }}} = the time in hrs for the boat to go upstream
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Going upstream:
(1) {{{ 24 = ( s - 3 )*t }}}
Going downstream:
(2) {{{ 24 = ( s + 3 )*( 6 - t ) }}}
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(2) {{{ 24 = 6s + 18 - s*t - 3t }}}
(2) {{{ 6s - s*t - 3t = 6 }}}
and
(1) {{{ s*t  = 3t + 24 }}}
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Substitute (1) into (2)
(2) {{{ 6s - 3t - 24 - 3t = 6 }}}
(2) {{{ 6t = 6s - 30 }}}
(2) {{{ t = s - 5 }}}
Substitute this back into (1)
(1) {{{ 24 = ( s - 3 )*( s-5 ) }}}
(1) {{{ 24 = s^2 - 8s + 15 }}}
(1) {{{ s^2 - 8s - 9 = 0 }}}
(1) {{{ ( s - 9 )*( s + 1 ) = 0 }}} ( by inspection )
{{{ s = 9 }}} ( can't use {{{ s = -1 }}} )
The boats speed is 9 mi/hr without a current
check:
(1) {{{ 24 = ( 9 - 3 )*t }}}
(1) {{{ 24 = 6t }}}
(1) {{{ t = 4 }}} hrs
and
(2) {{{ 24 = ( 9 + 3 )*( 6 - t ) }}}
(2) {{{ 24 = 12*( 6 - t ) }}}
(2) {{{ 24 = 72 - 12t }}}
(2) {{{ 12t = 72 - 24 }}}
(2) {{{ 12t = 48 }}}
(2) {{{ t = 4 }}} hrs
OK