Question 638934
Let {{{ s }}} = the speed of the boat without current
Let {{{ c }}} = the speed of the current
{{{ s - c }}} = speed going upstream
{{{ s + c }}} = speed going downstream
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Going upstream:
(1) {{{ 160 = ( s - c )*20 }}}
Going downstream:
(2) {{{ 160 = ( s + c )*5 }}}
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(1) {{{ 20s - 20c = 160 }}}
(1) {{{ s - c = 8 }}}
and
(2) {{{ 160 = 5s + 5c }}}
(2) {{{ s + c = 32 }}}
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Add (1) and (2)
(1) {{{ s - c = 8 }}}
(2) {{{ s + c = 32 }}}
{{{ 2s = 40 }}}
{{{ s = 20 }}}
and, since
(1) {{{ s - c = 8 }}}
(1) {{{ 20 - c = 8 }}}
(1) {{{ -c = -12 }}}
(1) {{{ c = 12 }}}
The speed of the boat without current is 20 mi/hr
The speed of the current is 12 mi/hr
check:
(1) {{{ 160 = ( 20 - 12 )*20 }}}
(1) {{{ 160 = 8*20 }}}
(1) {{{ 160 = 160 }}}
and
(2) {{{ 160 = ( 20 + 12 )*5 }}}
(2) {{{ 160 = 32*5 }}}
(2) {{{ 160 = 160 }}}
OK