Question 559322
Let {{{s}}} = speed of boat in still water
Let {{{c}}} = speed of current
{{{ s + c }}} = speed going downstream
{{{ s - c }}} = speed going upstream
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Going downstream:
(1) {{{ 210 = ( s + c )*10 }}}
Going upstream:
(2) {{{ 210 = ( s - c )*70 }}}
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(1) {{{ 10s + 10c = 210 }}}
(2) {{{ 70s - 70c = 210 }}}
Multiply both sides of (1) by {{{7}}}
and add the equations
(1) {{{ 70s + 70c = 1470 }}}
(2) {{{ 70s - 70c = 210 }}}
{{{ 140s = 1680 }}}
{{{ s = 12 }}}
and
(1) {{{ 10s + 10c = 210 }}}
(1) {{{ s + c = 21 }}}
(1) {{{ 12 + c = 21 }}}
(1) {{{ c = 9 }}}
12 mi/hr = speed of boat in still water
9 mi/hr = speed of current
check answer:
(2) {{{ 70s - 70c = 210 }}}
(2) {{{ s - c = 3 }}}
(2) {{{ 12 - 9 = 3 }}}
(2) {{{ 3 = 3 }}}
OK