Question 1011286
It's not really a "formula"
It's just catching on to a method
Just use [ distance ] = [ rate ] x [ time ]
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Let {{{ c }}} = the rate of the current in km/hr
{{{ 7 + c }}} = rate of the boat going downstream
{{{ 7 - c }}} = rate of the boat going upstream
Let {{{ t }}} = time in hrs for going either upstream or downstream
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Equation for going downstream:
(1) {{{ 30 = ( 7 + c )*t }}}
Equation for going upstream:
(2) {{{ 12 = ( 7 - c )*t }}}
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(1) {{{ t = 30 / ( 7 + c ) }}}
Substitute this into (2)
(2) {{{ 12 = ( 7 - c )*( 30 / ( 7 + c ) ) }}}
Multiply both sides by {{{ 7 + c }}}
(2) {{{ 12*( 7 + c ) = 30*( 7 - c ) }}}
(2) {{{ 84 + 12c = 210 - 30c }}}
(2) {{{ 42c = 126 }}}
(2) {{{ c = 3 }}}
The rate of the current is 3 km/hr
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check:
(1) {{{ 30 = ( 7 + c )*t }}}
(1) {{{ 30 = ( 7 +3 )*t }}}
(1) {{{ 30 = 10t }}}
(1) {{{ t = 3 }}}
and
(2) {{{ 12 = ( 7 - c )*t }}}
(2) {{{ 12 = ( 7 - 3 )*t }}}
(2) {{{ 12 = 4t }}}
(2) {{{ t = 3 }}}
OK