Question 1077395
Let {{{ t }}} = time spent going down river
{{{ 5 - t }}} = time spent going up river
Let {{{ r }}} = the rate of the boat in still water
{{{ r + 5 }}} = the rate of the boat going down riover
{{{ r - 5 }}} = the rate of the boat going up river
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Going down river:
(1) {{{ 60 = ( r+5 )*t }}}
Going up river:
(2) {{{ 60 = ( r-5 )*( 5-t ) }}}
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(1) {{{ t = 60/( r+5 ) }}}
and
(2) {{{ 60 = 5r - 25 - r*t + 5t }}}
(2) {{{ 60 = 5r - 25 + t*( 5-r ) }}}
Substitute (1) into (2)
(2) {{{ 60 = 5r - 25 + ( 60/( r+5 ))*( 5-r ) }}}
(2) {{{ 85 = 5r + ( 60/( r+5 ))*( 5-r ) }}}
Multiply both sides by {{{ r+5 }}}
(2) {{{ 85*( r+5 ) = 5r*( r+5 ) + 60*( 5-r ) }}}
(2) {{{ 85r + 425 = 5r^2 + 25r + 300 - 60r }}}
(2) {{{ 5r^2 - 120r - 125 = 0 }}}
(2) {{{ r^2 - 24r - 25 = 0 }}}
(2) {{{ ( r - 25 )*( r + 1 ) = 0 }}}
{{{ r = 25 }}} ( can't use the other solution )
The rate of the boat in still water is 25 mi/hr
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check:
(1) {{{ 60 = ( r+5 )*t }}}
(1) {{{ 60 = ( 25+5 )*t }}}
(1) {{{ 60 = 30t }}}
(1) {{{ t = 2 hrs
and
(2) {{{ 60 = ( r-5 )*( 5-t ) }}}
(2) {{{ 60 = ( 25-5 )*( 5-t ) }}}
(2) {{{ 60 = 20*( 5 - t ) }}}
(2) {{{ 3 = 5 - t }}}
(2) {{{ t = 2 }}} hrs
OK