Question 955155
Let {{{ c }}} = the rate of the current
{{{ 15 - c }}} = speed of boat going upstream
{{{ 15 + c }}} = speed of boat going downstream
{{{ t }}} = time in hours
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Going upstream:
(1) {{{ 8 = ( 15 - c )*t }}}
Going downstream:
(2) {{{ 12 = ( 15 + c )*t }}}
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(1) {{{ 8 = 15t - c*t }}}
(2) {{{ 12 = 15t + c*t }}}
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Add the equations
{{{ 20 = 30t }}}
{{{ t = 2/3 }}} hrs
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(1) {{{ 8 = ( 15 - c )*(2/3) }}}
(1) {{{ (3/2)*8 = 15 - c }}}
(1) {{{ 12 = 15 - c }}}
(1) {{{ c = 3 }}}
The rate of the current is 3 mi/hr
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check:
(2) {{{ 12 = ( 15 + c )*t }}}
(2) {{{ 12 = ( 15 + 3 )*(2/3) }}}
(2) {{{ 12 = 18*(2/3) }}}
(2) {{{ 12 = 12 }}}
OK