Question 876967
Let {{{ s }}} = the speed of the boat in still water
Going upstream:
(1) {{{ 5 = ( s - 4 )*t[1] }}}
Going downstream:
(2) {{{ 13 = ( s + 4 )*t[2] }}}
and
(3) {{{ t[1] + t[2] = 2 }}}
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(1) {{{ t[1] = 5 / ( s - 4 ) }}}
and
(2) {{{ t[2] = 13 / ( s + 4 ) }}}
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By substitution:
(3) {{{ 5 / ( s - 4 ) + 13 / ( s + 4 ) = 2 }}}
Multiply both sides by {{{ ( s - 4 )*( s + 4 ) }}}
(3) {{{ 5*( s + 4 ) + 13*( s - 4 ) = 2*( s^2 - 16 ) }}}
(3) {{{ 5s + 20 + 13s - 52 = 2s^2 - 32 }}}
(3) {{{ 2s^2 - 18s = 0 }}}
(3) {{{ s^2 - 9s = 0 }}}
(3) {{{ s*( s - 9 ) = 0 }}}
(3) {{{ s = 9 }}}
The speed of the boat in still water in 9 mi/hr
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check:
(1) {{{ 5 = ( s - 4 )*t[1] }}}
(1) {{{ 5 = ( 9 - 4 )*t[1] }}}
(1) {{{ t[1] = 1 }}}
and
(2) {{{ 13 = ( s + 4 )*t[2] }}}
(2) {{{ 13 = ( 9 + 4 )*t[2] }}}
(2) {{{ t[2] = 1 }}}
and
(3) {{{ t[1] + t[2] = 2 }}}
(3) {{{ 1 + 1 = 2 }}}
OK