Question 1033073
Let {{{ c }}} = the speed of the current in mi/hr
{{{ 10 + c }}} = boat's speed going downstream in mi/hr
{{{ 10 - c }}} = boat's speed going upstream in mi/hr
Let {{{ t }}} = time in hrs for both trips
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Equation for going downstream:
(1) {{{ 24 = ( 10 + c )*t }}}
Equation for going upstream:
(2) {{{ 16 = ( 10 - c )*t }}}
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(1) {{{ t = 24 / ( 10 + c ) }}}
and
(2) {{{ 16 = ( 10 - c )*( 24 / ( 10 + c ) ) }}}
(2) {{{ 16*( 10 + c ) = 24*( 10 - c ) }}}
(2) {{{ 160 + 16c = 240 - 24c }}}
(2) {{{ 40c = 80 }}}
(2) {{{ c = 2 }}}
The rate of the current is 2 mi/hr
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check:
(1) {{{ 24 = ( 10 + 2 )*t }}}
(1) {{{ t = 24 / 12 }}}
(1) {{{ t = 2 }}} hrs
and
(2) {{{ 16 = ( 10 - 2 )*t }}}
(2) {{{ 16 = 8t }}}
(2) {{{ t = 2 }}} hrs
OK