Question 584651
Let {{{ s }}} = the speed of the boat in still water
Let {{{ c }}} = the speed of the current
{{{ s + c }}} = the speed of the boat going with the current
{{{ s - c }}} = the speed of the boat going against the current
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(1) {{{ 15 = ( s + c )*1 }}}
(2) {{{ 15 = ( s - c )*(5/3) }}}
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(1) {{{ s + c = 15 }}}
and
(2) {{{ s - c = (3/5)*15 }}}
(2) {{{ s - c = 9 }}}
Add the equations
(1) {{{ s + c = 15 }}}
(2) {{{ s - c = 9 }}}
{{{ 2s = 24 }}}
{{{ s = 12 }}}
and, since
(1) {{{ s + c = 15 }}}
(1) {{{ 12 + c = 15 }}}
(1) {{{ c = 3 }}}
The speed of the boat in still water is 12 mi/hr
The speed of the current is 3 mi/hr
check:
(2) {{{ 15 = ( 12 - 3 )*(5/3) }}}
(2) {{{ 15 = 9*(5/3) }}}
(2) {{{ 15 = 15 }}}
OK