Question 734756
Let the time for each of the 2 trips = {{{ t }}} hrs
Let the speed of the boat in still water = {{{ s }}}
The boat's speed going downstream = {{{ s + 5 }}} mi/hr
The boat's speed going upstream = {{{ s - 5 }}} mi/hr
-------------
Equation for downstrteam trip:
(1) {{{ 72 = ( s + 5 )*t }}}
Equation for upstrteam trip:
(2) {{{ 36 = ( s - 5 )*t }}}
--------------------
(1) {{{ 72 = s*t + 5t }}}
and
(2) {{{ 36 = s*t - 5t }}}
-------------------
(2) {{{ s*t = 36 + 5t  }}}
Substitute (2) into (1)
(1) {{{ 72 = 36 + 5t + 5t }}}
(1) {{{ 10t = 36 }}}
(1) {{{ t = 3.6 }}}
and
(2) {{{ 36 = ( s - 5 )*3.6 }}}
(2) {{{ 10 = s - 5 }}}
(2) {{{ s = 15 }}}
The speed of the boat in still water is 15 mi/hr
check:
(1) {{{ 72 = s*t + 5t }}}
(1) {{{ 72 = 15t + 5t }}}
(1) {{{ 72 = 20t }}}
(1) {{{ t = 3.6 }}} 
OK
(2) {{{ 36 = s*t - 5t }}}
(2) {{{ 36 = 15t - 5t }}}
(2) {{{ 36 = 10t }}}
(2) {{{ t = 3.6 }}}
OK