Question 413508
Let {{{a}}} = car A's speed
Let {{{b}}} = car B's speed
Moving towards each other, just add the speeds
{{{6.6 = (a + b)*1}}}
{{{a + b = 6.6}}}
{{{b = 6.6 - a}}}
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In the same direction:
car A:
(1) {{{d = a*11}}}
car B:
{{{d + 6.6 = b*11}}}
(2) {{{d = 11b - 6.6}}}
B overtakes A, so it is the one that has to make up 
the 6.6 mi between them
Since {{{d}}} is the same in both equations,
{{{11a = 11b - 6.6}}}
and,  from above,
{{{b = 6.6 - a}}}
By substitution:
{{{11a = 11*(6.6 - a) - 6.6}}}
{{{11a = 72.6 - 11a - 6.6}}}
{{{22a = 66}}}
{{{a = 3}}}
{{{b = 6.6 - a}}}
{{{b = 3.6}}}
A's speed is 3 mi/hr
B's speed is 3.6 mi/hr
check answer:
going towards each other:
{{{d[A] = 3*1}}}
{{{d[B] = 3.6*1}}}
{{{d[A] + d[B] = 6.6}}} 
OK
same direction:
car A:
(1) {{{d = 3*11}}}
{{{d = 33}}}
car B:
{{{d + 6.6 = 3.6*11}}}
{{{d = 39.6 -6.6}}}
{{{d = 33}}}
OK