Question 703538
Let {{{ s }}} = the rate of the canoe in still water in km/hr
Let {{{ c }}} = the rate of the current in km/hr
{{{ s + c }}} = the canoe's rate going with the current in km/hr
{{{ s - c }}} = the canoe's rate going against the current in km/hr
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Going with the current:
(1) {{{ 48 = ( s + c )*3 }}}
Going against the current:
(2) {{{ 48 = ( s - c )*4 }}}
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(1) {{{ 3s + 3c = 48 }}}
(1) {{{ s + c = 16 }}}
and
(2) {{{ 4s - 4c = 48 }}}
(2) {{{ s - c = 12 }}}
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Add (1) and (2)
(1) {{{ s + c = 16 }}}
(2) {{{ s - c = 12 }}}
{{{ 2s = 28 }}}
{{{ s = 14 }}}
and
(2) {{{ s - c = 12 }}}
(2) {{{ 14 - c = 12 }}}
(2) {{{ c = 2 }}}
The rate of the canoeist in still water is 14 km/hr
The rate of the current is 2 km/hr
check answer:
(1) {{{ 48 = ( s + c )*3 }}}
(1) {{{ 48 = ( 14 + 2 )*3 }}}
(1) {{{ 48 = 16*3 }}}
(1) {{{ 48 = 48 }}}
and
(2) {{{ 48 = ( s - c )*4 }}}
(2) {{{ 48 = ( 14 - 2 )*4 }}}
(2) {{{ 48 = 12*4 }}}
(2) {{{ 48 = 48 }}}
OK