Question 1061532
Let d be the distance (in meters) between cities A and B.
Time in minutes and speed in meters per minute (m/ min)

Using formula, distance = speed *  time 
                  d= v * t

let @ time t minutes Nora meets Kate.

         d= 100*t + 80*t   
         d= 180* t   (1) 
('d' is point @ kate and nora meet each other= Distance covered by Nora + distance covered Kate)

Similarly, @ time (t+6) minues Nora meets Lixin

        d= 100*(t+6) + 75*(t+6)   ( here (t+6) is common)
        d= 175*(t+6)   
        d= 175*t + 1050    (2) 

Equating (1) and (2)  
                   d   =   d 

                  180 t = 175 t+ 1050
On simplifying,
                  180t - 175t = 1050

                           5t = 1050
                            t=210 minutes

@ time = 210 minutes Nora met Kate
Also,@ time (210+6=) 216 minutes Nora met Lixin

Using, the value to t and substituting in equation (1)
                      d= 180* 210 m (here minutes will be cancelled by minutes)

                  d= 18*21*100 m = 37800 metrea

The distance between the cities A and B is 37800 meters.