Question 621016
Let {{{ s }}} = the speed of the tugboat without a current
Let {{{ c }}} = the speed of the current
Going upstream:
(1) {{{ 160 = ( s - c )*20 }}}
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Going downstream:
(2) {{{ 160 = ( s + c )*10 }}}
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(1) {{{ s - c = 8 }}}
and
(2) {{{ s + c = 16 }}}
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Add (1) and (2)
(1) {{{ s - c = 8 }}}
(2) {{{ s + c = 16 }}}
{{{ 2s = 24 }}}
{{{ s = 12 }}}
and, since
(1) {{{ s - c = 8 }}}
(1) {{{ 12 - c = 8 }}}
(1) {{{ -c =-4 }}}
(1) {{{ c = 4 }}}
The speed of the tugboat without a current is 12 mi/hr
The speed of the current is 4 mi/hr
check:
(1) {{{ 160 = ( s - c )*20 }}}
(1) {{{ 160 = ( 12 - 4 )*20 }}}
(1) {{{ 160 = 8*20 }}}
(1) {{{ 160 = 160 }}}
OK