Question 515181
Let {{{c}}} = speed of current
Let {{{s}}} = speed of boat in still water
given:
Going downstream:
(1) {{{ 114 = ( s + c )*t }}}
Going upstream:
(2) {{{ 24 = ( s - c )*t }}}
-------------------
(1) {{{ 114 = ( 23 + c )*t }}}
(2) {{{ 24 = ( 23 - c )*t }}}
-------------------
(1) {{{ 114 = 23t + c*t }}}
(2) {{{ 24 = 23t - c*t }}}
Add the equations
{{{ 138 = 46t }}}
{{{ t = 3 }}}
and, since
(1) {{{ 114 = 23t + c*t }}}
(1) {{{ 114 = 23*3 + 3c }}}
(1) {{{ 3c = 114 - 69 }}}
(1) {{{ 3c = 45 }}}
(1) {{{ c = 15 }}}
The speed of the current is 15 mi/hr
check:
(2) {{{ 24 = ( s - c )*t }}}
(2) {{{ 24 = ( 23 - 15 )*3 }}}
(2) {{{ 24 = 8*3 }}}
(2) {{{ 24 = 24 }}}
OK