Question 856197
Let {{{ c }}} = the speed of the current
{{{ 10 - c }}} = the boat's speed going upstream
{{{ 10 + c }}} = the boat's speed going downstream
Let {{{ t }}} = the time in hours for both trips
-----------------------------------------
Equation for going upstream:
(1) {{{ 16 = ( 10 - c )*t }}}
Equation for going downstream:
(2) {{{ 24 = ( 10 + c )*t }}}
-----------------------
Add the equations:
(1) {{{ 16 = 10t - c*t }}}
(2) {{{ 24 = 10t + c*t }}}
{{{ 20t = 40 }}}
{{{ t = 2 }}} hrs
------------------
(1) {{{ 16 = ( 10 - c )*2 }}}
(1) {{{ 10 - c = 8 }}}
(1) {{{ c = 2 }}}
The speed of the current is 2 mi/hr
check:
(2) {{{ 24 = ( 10 + c )*t }}}
(2) {{{ 24 = ( 10 + 2 )*2 }}}
(2) {{{ 24 = 12*2 }}}
(2) {{{ 24 = 24 }}}
OK