Question 982496
Charlie has a speed due to his rowing and the current,
but the driftwood only has speed due to the current
Let {{{ s }}} = Charlie's speed without the current
Let {{{ c }}} = the speed of the current
{{{ s + c }}} = Charlie's speed going downstream
{{{ s - c }}} = charlie's speed going upstream
Let {{{ d }}} = distance from Amaroo to Bradden in km
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Equation for going downstream:
(1) {{{ d = ( s + c )*3 }}}
Equation for going upstream:
(2) {{{ d = ( s - c )*4 }}}
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Plug (1) into (2)
(3) {{{ ( s + c )*3 = ( s - c )*4 }}}
{{{ 3s + 3c = 4s - 4c }}}
{{{ s = 7c }}}
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Add (1) and (2)
{{{ 2d = 7s - c }}}
{{{ 2d = 7*7c - c }}}
{{{ 2d = 48c }}}
{{{ d = c*( 24 ) }}}
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It takes 24 hrs for the driftwood to float downstream
check:
(1) {{{ d = ( s + c )*3 }}}
(1) {{{ d = ( s + d/24 )*3 }}}
(1) {{{ d = 3s + d/8 }}}
(1) {{{ (7/8)*d = 3s }}}
(1) {{{ d = s*(24/7) }}}
and
(2) {{{ d = ( s - d/24 )*4 }}}
(2) {{{ d = 4s - d/6 }}}
(2) {{{ (7/6)*d = 4s }}}
(2) {{{ d = (6/7)*4s }}}
(2) {{{ d = s*(24/7) }}}
OK
Hope I got it!