Question 1055078
Let {{{ s }}} = the speed of the boat in still water
{{{ s - 5 }}} = the speed of the boat going upstream
{{{ s + 5 }}} = the speed of the boat going downstream
Let {{{ t }}} = time in hrs for traveling both upstream and downstream
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equation for going upstream:
(1) {{{ 2 = ( s-5 )*t }}}
equation for going downstream:
(2) {{{ 12 = ( s + 5 )*t }}}
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(1) {{{ t = 2/( s-5 ) }}}
Plug (1) into (2)
(2) {{{ 12 = ( s+5 )*( 2/( s-5 )) }}}
(2) {{{ 12*( s-5 ) = 2*( s+5 ) }}}
(2) {{{ 12s - 60 = 2s + 10 }}}
(2) {{{ 10s = 70 }}}
(2) {{{ s = 7 }}}
The speed of the boat is still water is 7 mi/hr
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check:
(1) {{{ 2 = ( s-5 )*t }}}
(1) {{{ 2 = ( 7-5 )*t }}}
(1) {{{ 2 = 2t }}}
(1) {{{ t = 1 }}} hr
and
(2) {{{ 12 = ( s + 5 )*t }}}
(2) {{{ 12 = ( 7 + 5 )*t }}}
(2) {{{ 12 = 12t }}}
(2) {{{ t = 1 }}} hr
OK