Question 692747
Let {{{ c }}} = the rate of the current in mi/hr
Let {{{ b }}} = the rate of the boat in still water in mi/hr
{{{ b + c }}} = the rate of the boat going downstream in mi/hr
{{{ b - c }}} = the rate of the boat going upstream in mi/hr
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Convert {{{ 70 }}} min to hrs.
{{{ 70/60 = 7/6 }}} hrs
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Equation for going downstream:
(1) {{{ 10 = ( b + c )*(7/6) }}}
Equation for going upstream:
(2) {{{ 10 = ( b - c )*2 }}}
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This is 2 equations with 2 unknowns, so it's solvable
(2) {{{ 10 = 2b - 2c }}}
(2) {{{ 5 = b - c }}}
(2) {{{ b = c + 5 }}}
Substitute this into (1)
(1) {{{ 10 = ( c + 5 + c )*(7/6) }}}
(1) {{{ 10 = ( 2c + 5 )*(7/6) }}}
(1) {{{ 10 = (7/3)*c + 35/6 }}}
(1) {{{ (7/3)*c = 60/6 - 35/6 }}}
(1) {{{ (14/6)*c = 25/6 }}}
(1) {{{ 14c = 25 }}}
(1) {{{ c = 25/14 }}}
(1) {{{ c = 1.7857 }}}
and, since
(2) {{{ b = c + 5 }}}
(2) {{{ b = 1.7857 + 5 }}}
(2) {{{ b = 6.7857 }}}
The rate of the boat is 6.7857 mi/hr
The rate of the current is 1.7857 mi/hr
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check:
(2) {{{ 10 = ( b - c )*2 }}}
(2) {{{ 10 = ( 6.7857 - 1.7857 )*2 }}}
(2) {{{ 10 = 5*2 }}}
(2) {{{ 10 = 10 }}}
OK
(1) {{{ 10 = ( b + c )*(7/6) }}}
(1) {{{ 10 = ( 6.7857 + 1.7857 )*(7/6) }}}
(1) {{{ 10 =  8.5714*(7/6) }}}
(1) {{{ 60 = 8.5714*7 }}}
(1) {{{ 60 = 59.9998 }}}
error must be due to rounding off- OK