Question 891914
Let {{{ c }}} = the rate of the current in mi/hr
Let {{{ s }}} = the speed of the boat in still water
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Going downstream:
(1) {{{ 36 = ( s + c )*2 }}}
Going upstream:
(2) {{{ 36 = ( s - c )*3 }}}
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(1) {{{ 2s + 2c = 36 }}}
(2) {{{ 3s - 3c = 36 }}}
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(1) {{{ s + c = 18 }}}
(2) {{{ s - c = 12 }}}
Add the equations
{{{ 2s = 30 }}}
{{{ s = 15 }}}
and
(1) {{{ 15 + c = 18 }}}
(1) {{{ c = 3 }}}
The rate of the boat in still water is 15 mi/hr
The speed of the current is 3 mi/hr
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check:
(1) {{{ 36 = ( s + c )*2 }}}
(1) {{{ 36 = ( 15 + 3 )*2 }}}
(1) {{{ 36 = 18*2 }}}
(1) {{{ 36 = 36 }}}
and
(2) {{{ 36 = ( s - c )*3 }}}
(2) {{{ 36 = ( 15 - 3 )*3 }}}
(2) {{{ 36 = 12*3 }}}
(2) {{{ 36 = 36 }}}
OK