SOLUTION: Alice and Bob started to walk towards each other’s home and then back to theirs, with steady speeds. Alice passed by a bus station at 25 m away from her home, while at the same tim

Let  S  be the distance between their homes, in meters.

Let    be Alice's rate, and   be Bob's rate.

Let    be the time after their start to their first meeting.

Let    be the time after their start to their second meeting.


     Notice I follow your  (your ?)  designations in your  (your ?)  set up in

          https://math.stackexchange.com/questions/2859310/distances-and-speeds

          https://math.stackexchange.com/questions/2859310/distances-and-speeds


Then you have 

     = S - 55;      = 55;           (1)

     = 2S - 85;      = S + 85.      (2)


From (1) you have   = ;               (3)

From (2) you have   = ,              (4)

which gives you an equation for S


     = .


Simplify and solve for S:

    (S-55)*(S+85) = (2S-85)*55

    S^2 -55*S + 85*S - 55*85 = 110*S - 55*85

    S^2 - 55*S + 85*S - 110*S = 0

    S^2 - 80*S = 0

    S*(S-80) = 0  ====>  The only positive root is   S = 80.


Thus we found the distance between the homes: it is 80 meters.


Having this known,  you van calculate the ratio of their rates from (3)

     =  =  =    

and hence calculate the distance "x" from the Bob's home to the abandoned car from the proportion

     =   ======>  x =  = 55 m.


Then the distance under the question is  80 - 25 - 55 meters = 0 meters.