Question 841574
Let {{{ c }}} = the speed of the current in mi/hr
Let {{{ t }}} = his time for rowing upstream in hrs
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Equation for rowing upstream:
(1) {{{ 6 = ( 5 - c )*t }}}
Equation for rowing downstream:
(2) {{{ 10 = ( 5 + c )*(1/3)*t }}}
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(1) {{{ 6 = 5t - c*t }}}
and
(2) {{{ 10 = (5/3)*t + (1/3)*c*t }}}
(2) {{{ 30 = 5t + c*t }}}
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(2) {{{ c*t = -5t + 30 }}}
(2) {{{ c = ( -5t + 30 ) / t }}}
substitute (2) into (1)
(1) {{{ 6 = 5t - c*t }}}
(1) {{{ 6 = 5t - (( -5t + 30 )/t )*t }}}
(1) {{{ 6 = 5t - ( -5t + 30 ) }}}
(1) {{{ 6 = 5t + 5t - 30 }}}
(1) {{{ 10t = 36 }}}
(1) {{{ t = 3.6 }}} hrs
and
(1) {{{ 6 = ( 5 - c )*t }}}
(1) {{{ 6 = ( 5 - c )*3.6 }}}
(1) {{{ 5 - c = 5/3 }}}
(1) {{{ c = 5 - 5/3 }}}
(1) {{{ c = 10/3 }}}
The speed of the current is 3.333 miles/hr
check:
(2) {{{ 10 = ( 5 + c )*(1/3)*t }}}
(2) {{{ 10 = ( 5 + 10/3 )*(1/3)*t }}}
(2) {{{ 10 = ( 25/3 )*(1/3)*t }}}
(2) {{{ 25t = 90 }}}
(2) {{{ t = 3.6 }}} hrs
and
(1) {{{ 6 = ( 5 - c )*t }}}
(1) {{{ 6 = ( 5 - 10/3 )*t }}}
(1) {{{ 6 = ( 5/3 )*t }}}
(1) {{{ t = (3/5)*6 }}}
(1) {{{ t = 3.6 }}} hrs
OK