Question 641755
Let {{{ c }}} = the speed of the current
{{{ 3 + c }}} = dog's speed going downstream
{{{ 3 - c }}} = dog's speed going upstream
Let {{{ t }}} = dog's time to travel downstream
{{{ 12 - t }}} = dog's time to travel upstream
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Equation going downstream:
(1) {{{ 10 = ( 3 + c )*t }}}
Equation going upstream:
(2) {{{ 10 = ( 3 - c )*( 12 - t ) }}}
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(1) {{{ t = 10 / ( 3 + c ) }}}
and
(2) {{{ 10 = 36 - 12c - 3t + c*t }}}
Substitute (1) into (2)
(2) {{{ 10 = 36 - 12c - 3*10 / ( 3 + c ) + 10c / ( 3 + c ) }}}
(2) {{{ -26 =  - 12c - 30 / ( 3 + c ) + 10c / ( 3 + c ) }}}
Multiply both sides by {{{ 3 + c }}}
(2) {{{ -26*( 3 + c ) = -12c*( 3 + c ) - 30 + 10c }}}
Multiply both sides by {{{ -1 }}}
(2) {{{ 78 + 26c = 36c + 12c^2 + 30 - 10c }}}
(2) {{{ 12c^2 = 48 }}}
(2) {{{ c^2 = 4 }}}
(2) {{{ c = 2 }}}
The speed of the current is 2 mi/hr
check:
(1) {{{ 10 = ( 3 + 2 )*t }}}
(1) {{{ t = 10/5 }}}
(1) {{{ t = 2 }}} hrs
and
(2) {{{ 10 = ( 3 - 2 )*( 12 - t ) }}}
(2) {{{ 10 = 12 - t }}}
(2) {{{ t = 2 }}} hrs
OK- I get the same answer