Question 1081853
Let {{{ s }}} = the speed of the boat in still water in km/hr
Let {{{ t }}} = time in hrs to travel 10 km in river B
{{{ 2t }}} = time in hrs to travel 18 km in river A
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Equation for going upstream in river A:
(1) {{{ 18 = ( s - 3 )*2t }}}
Equation for going upstream in river B:
(2) {{{ 10 = ( s - 1 )*t }}}
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(2) {{{ t = 10/( s - 1 ) }}}
Plug this result into (1)
(1) {{{ 18 = ( s - 3 )*2*( 10/( s - 1 )) }}}
(1) {{{ 18*( s - 1 ) = 20*( s - 3 ) }}}
(1) {{{ 18s - 18 = 20s - 60 }}}
(1) {{{ 2s = 42 }}}
(1) {{{ s = 21 }}}
The speed of the boat in still water is 21 km/hr
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check:
(1) {{{ 18 = ( s - 3 )*2t }}}
(1) {{{ 18 = ( 21 - 3 )*2t }}}
(1) {{{ 18 = 18*2t }}}
(1) {{{ t = .5 }}} hrs
and
(2) {{{ 10 = ( s - 1 )*t }}}
(2) {{{ 10 = ( 21 - 1 )*t }}}
(2) {{{ 10 = 20t }}}
(2) {{{ t = .5 }}} hrs
OK