Question 701751
Let {{{ s }}} = their speed in still water in mi/hr
{{{ s + 5 }}} = tugboat's speed going with the current in mi/hr
{{{ s - 5 }}} = tugboat's speed going against the current in mi/hr
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Equation for tugboat going upstream:
(1) {{{ 6 = ( s - 5 )*t }}}
Equation for tugboat going downstream:
(2) {{{ 30 = ( s + 5 )*t }}}
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(1) {{{ 6 = s*t - 5t }}}
(2) {{{ 30 = s*t + 5t }}}
Subtract (1) from (2)
(2) {{{ 30 = s*t + 5t }}}
(1) {{{ -6 = -s*t + 5t }}}
{{{ 24 = 10t }}}
{{{ t = 2.4 }}} hrs
and
(1) {{{ 6 = ( s - 5 )*2.4 }}}
(1) {{{ 6 = 2.4s - 12 }}}
(1) {{{ 2.4s = 18 }}}
(1) {{{ s = 7.5 }}}
Their speeds in still water is 7.5 mi / hr
check:
(2) {{{ 30 = ( s + 5 )*t }}}
(2) {{{ 30 = ( 7.5 + 5 )*2.4 }}}
(2) {{{ 30 = 12.5*2.4 }}}
(2) {{{ 30 = 30 }}}
OK
(1) {{{ 6 = ( s - 5 )*t }}}
(1) {{{ 6 = ( 7.5 - 5 )*2.4 }}}
(1) {{{ 6 = 2.5*2.4 }}}
(1) {{{ 6 = 6 }}}
OK