Question 1163985
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<pre>

Let d be the distance between the cities, in kilometres.


Then the rate of train A is  {{{d/8}}}  km/h;  the rate of the train B is  {{{d/12}}} km/h.


The time from the start to the meeting point is the same, so the traveled distances  {{{d[A]}}}  and  {{{d[B]}}}
by the trains are in the same ratio as their rates


    {{{d[A]/d[B]}}} = {{{((d/8))/((d/12))}}} = {{{12/8}}} = {{{3/2}}}.


It implies  that the distance traveled by train A before they met was  {{{d*(3/(3+2))}}} = {{{(3/5)d}}};

                 the distance traveled by train B before they met was  {{{d*(2/(3+2))}}} = {{{(2/5)d}}}.


We are given that

    {{{(3/5)d}}} - {{{(2/5)d}}} = 192.


It means that

    {{{(1/5)d}}} = 192;


hence,  d = 5*192 = 960 kilometers.


<U>ANSWER</U>.  The distance between the cities is 960 kilometers.
</pre>

Solved.