Question 971136
Let {{{ c }}} = the speed of the current in mi/hr
{{{ 23 - c }}} = the boat's speed going upstream in mi/hr
{{{ 23 + c }}} = the boat's speed going downstream in mi/hr
Let {{{ d }}} = the one-way distance in mi
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Going upstream:
(1) {{{ d = ( 23 - c )*(29/60) }}}
( note that I converted minutes to hours )
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Going downstream:
(2) {{{ d = ( 23 + c )*(17/60) }}}
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Substitute (2) into (1)
(1) {{{ ( 23 + c )*(17/60) = ( 23 - c )*(29/60) }}}
Multiply both sides by {{{ 60 }}}
(1) {{{ 17*23 + 17c = 23*29  - 29c }}}
(1) {{{ 46c = 23*( 29 - 17 ) }}}
(1) {{{ 46c = 23*12 }}}
(1) {{{ 46c = 276 }}}
(1) {{{ c = 6 }}}
The speed of the current is 6 mi/hr
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check:
(1) {{{ d = ( 23 - c )*(29/60) }}}
(1) {{{ d = ( 23 - 6 )*(29/60) }}} 
(1) {{{ d = 17*( 29/60) }}}
(1) {{{ d = 493/60 }}}
(1) {{{ d = 8.21667 }}} mi
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(2) {{{ d = ( 23 + 6 )*(17/60) }}}
(2) {{{ d = 29*(17/60) }}}
(2) {{{ d = 493/60 }}}
(2) {{{ d = 8.21667 }}} mi
OK