Question 1000200
Let {{{ r }}} = the speed of the river in km/hr
{{{ 20 + r }}} = the speed of the paddleboat going downstream in km/hr
{{{ 20 - r }}} = th speed of the paddleboat going upstream in km/hr
Let {{{ t }}} = time in hrs to go upstream or downstream
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Going downstream:
(1) {{{ 6 = ( 20 + r )*t }}}
Going upstream:
(2) {{{ 3 = ( 20 - r )*t }}}
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(1) {{{ t = 6/( 20+r ) }}}
and
(2) {{{ t = 3/( 20-r ) }}}
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{{{ 6/( 20+r ) = 3/( 20-r ) }}}
{{{ 6*( 20-r ) = 3*( 20+r ) }}}
{{{ 120 - 6r = 60 + 3r }}}
{{{ 9r = 60 }}}
{{{ r = 20/3 }}}
{{{ r = 6.667 }}} km/hr
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check answer:
(1) {{{ t = 6/( 20+r ) }}}
(1) {{{ t = 6/( 20+6.667 ) }}}
(1) {{{ t = 6/26.667 }}}
and
(2) {{{ t = 3/( 20-r ) }}}
(2) {{{ t = 3/( 20-6.667 ) }}}
(2) {{{ t = 3/13.333 }}}
(2) {{{ t = 6/26.667 }}}
OK