Question 1201875
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x = slower speed
x+k = faster speed
where k is some positive real number, k > 0


{{{d[1]}}} = distance traveled by the slower car
{{{d[2]}}} = distance traveled by the faster car


Slower car:
distance = rate*time
d = r*t
{{{d[1]}}} = x*2
{{{d[1]}}} = 2x


Faster car:
d = r*t
{{{d[2]}}} = (x+k)*2
{{{d[2]}}} = 2x+2k
{{{d[2]}}} = {{{d[1]}}}+2k


Their individual travel distances add together to get the total distance between them, because the cars travel in opposite directions. 
Draw out a number line to see why this is the case.
I'll assume the cars start off at the same location.
{{{d[1]}}}+{{{d[2]}}} = 110
2x+2x+2k = 110
4x+2k = 110
2(2x+k) = 110
2x+k = 110/2
2x+k = 55
2x = 55-k
{{{d[1]}}} = 55-k
If we knew the value of k, then we can find the distance the slower car traveled.


To avoid {{{d[1]}}} being zero or negative, we must have 55-k > 0 which leads to k < 55


Earlier it was mentioned that k > 0
So 0 < k < 55
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