Question 1130823
let {{{s }}} = the speed of the boat in still water in km/hr
Let {{{ w }}} = the speed of the current in km/hr
Going upstream:
(1) {{{ 100 = ( s - w )*5 }}}
Going downstream:
(2) {{{ 100 = ( s + w )*2 }}}
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(1) {{{ 5s - 5w = 100 }}}
(2) {{{ 2s + 2w = 100 }}}
Multiply (1) by {{{2 }}}, multiply
(2) by {{{ 5 }}}, and add the equations
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(2) {{{ 10s + 10w = 500 }}}
(1) {{{ 10s - 10w = 200 }}}
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{{{ 20s = 700 }}}
{{{ s = 35 }}}
and
(2) {{{ 2*35 + 2*w = 100 }}}
(2) {{{ 2w = 30 }}}
(2) {{{ w = 15 }}}
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Rate in still water: 35 km/hr
Rate of the current: 15 km/hr