Question 328438
You need 2 equations:
{{{d[A] = r[A]*t{A]}}}
{{{230 = (r[B] - 8)*t[A]}}}
and
{{{d[B] = r[B]*t[B]}}}
{{{270 = r[B]*t[B]}}}
You are given that {{{t[A] = t[B]}}}, so
{{{230/(r[B] - 8) = 270/r[B]}}}
Multiply both sides by {{{r[B]*(r[B] - 8)}}}
{{{230r[B] = 270*(r[B] - 8)}}}
{{{230r[B] = 270r[B] - 2160}}}
{{{40r[B] = 2160}}}
{{{r[B] = 54}}}
and, since
{{{r[A] = r[B] - 8}}}
{{{r[A] = 54 - 8}}}
{{{r[A] = 46}}}
The speed of train A is 46 mi/hr
The speed of train B is 54 mi/hr
check answers:
{{{d[A] = r[A]*t[A]}}}
{{{230 = 46*t[A]}}}
{{{t[A] = 230/46}}}
{{{t[A] = 5}}} hrs
and
{{{d[B] = r[B]*t[B]}}}
{{{270 = 54*t[B]}}}
{{{t[B] = 270/54}}}
{{{t[B] = 5}}} hrs
{{{t[A] = t[B]}}} 
OK