Question 760024
Let {{{ s }}} = the speed of the boat in still water in mi/hr
Let {{{ c }}} = the speed of the current in mi/hr
{{{ s - c }}} = the speed of the boat going upriver
{{{ s + c }}} = the speed of the boat going downriver
Let {{{ d }}} = the one-way distance the boat travels
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Going upriver:
(1) {{{ d = ( s - c )*6 }}}
Going downriver:
(2) {{{ d = ( s + c )*4 }}}
and, also given:
(3) {{{ s + c = s - c + 6 }}}
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(3) {{{ c = -c + 6 }}}
(3) {{{ 2c = 6 }}}
(3) {{{ c = 3 }}} mi/hr
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By substitution:
(2) {{{ ( s-c )*6 = ( s + c )*4 }}}
(2) {{{ ( s-3 )*6 = ( s + 3 )*4 }}}
(2) {{{ 6s - 18 = 4s + 12 }}}
(2) {{{ 2s = 30 }}}
(2) {{{ s = 15 }}}
The speed of the boat in still water is 15 mi/hr
check:
(1) {{{ d = ( s - c )*6 }}}
(1) {{{ d = ( 15 - 3 )*6 }}}
(1) {{{ d = 72 }}} mi
and
(2) {{{ d = ( s + c )*4 }}}
(2) {{{ d = ( 15 + 3 )*4 }}}
(2) {{{ d = 72 }}} mi
OK