Question 445757
Let {{{c}}} = the rate of the current
Let {{{b}}} = the speed of the boat in still water
given:
{{{ d= 144 km }}}
time going upstream: {{{ t[1] = 3}}} hrs
time going downstream: {{{ t[2] = 2 }}} hrs
The equation going upstream:
{{{ d = ( b - c )*t[1] }}}
(1) {{{ 144 = ( b - c )*3 }}}
The equation going downstream:
{{{ d = ( b + c )*t[2] }}}
(2) {{{ 144 = ( b + c )*2 }}}
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There are 2 equations and 2 unknowns, so
it should be solvable
(1) {{{ 144 = ( b - c )*3 }}}
(1) {{{ 3b - 3c = 144 }}}
and
(2) {{{ 144 = ( b + c )*2 }}}
(2) {{{ 2b + 2c = 144 }}}
Multiply both sides of (1) by {{{2}}}
and both sides of (2) by {{{3}}} and
subtract (1) from (2)
(2) {{{ 6b + 6c = 432 }}}
(1) {{{ -6b + 6c = -288 }}}
{{{ 12c = 144 }}}
{{{ c = 12 }}} km/hr
and
(2) {{{ 2b + 2c = 144 }}}
(2) {{{ 2b + 2*12 = 144 }}}
(2) {{{ 2b = 144 - 24 }}}
(2) {{{ 2b = 120 }}}
{{{ b = 60 }}} km/hr
12 km/hr is the rate of the current
60 km/hr is the speed of the boat in still water