Question 737528
Let {{{ d }}} = distance red car has traveled
{{{ 305 - d }}} = distance blue car has traveled
{{{ r }}} = time for red car
{{{ b }}} = time for blue car
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One of the cars must have been traveling for 
{{{ 5 }}} hrs, the other for less time
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red car:
(1) {{{ d = 55*r }}}
blue car:
(2) {{{ 305 - d = 65*b }}}
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(2) = {{{ d = 305 - 65b }}}
By substitution:
{{{ 55r = 305 - 65b }}}
{{{ 11r + 13b = 61 }}} 
The red car had to be the one traveling for {{{ 5 }}},
since {{{ 13*5 = 65 }}} is too much, so
{{{ 11*5 + 13b = 61 }}}
{{{ 13b = 61 - 55 }}}
{{{ 13b = 6 }}}
{{{ b = 6/13 }}} hrs
The red car drove for 5 hrs, the blue car drove for 6/13 hrs
check:
(1) {{{ d = 55*r }}}
(1) {{{ d = 55*5 }}}
(1) {{{ d = 275 }}}
and
(2) {{{ 305 - d = 65*b }}}
(2) {{{ 305 - 275 = 65*(6/13) }}}
(2) {{{ 30 = 30 }}}
OK