a and b are 90km apart …

Let X and Y be two cars starting from points A and B respectively. Let the speed of car X be x km/hr and that of car Y be y km/hr.
CASE I : 

When two cars move in the same directions:
Suppose two cars meet at point Q. Then,
Distance travelled by car {tex}X = AQ{/tex},
Distance travelled by car {tex}Y = BQ.{/tex}
{tex}\therefore{/tex} Distance travelled by car X in 9 hours = {tex}9x\ km.{/tex}
and {tex}BQ = 9y{/tex}

Clearly, {tex}AQ - BQ =AB{/tex}
{tex}\Rightarrow{/tex}{tex}9x - 9y =90{/tex}
{tex}\Rightarrow{/tex}{tex}x - y =10{/tex} [{tex}\because{/tex} {tex}AB = 90\ km{/tex}]
CASE II

When two cars move in opposite directions:
Suppose two cars meet at point P. Then,
Distance travelled by car {tex}X = AP{/tex},
Distance travelled by car {tex}Y = BP{/tex},
{tex}\therefore{/tex} Distance travelled by car X in {tex}\frac { 9 } { 7 }{/tex} hours {tex}= \frac { 9 } { 7 }{/tex} x km
and {tex}B P = \frac { 9 } { 7 } y{/tex}
{tex}AP + BP =AB{/tex}
{tex}\Rightarrow{/tex}{tex}\frac { 9 } { 7 } x + \frac { 9 } { 7 } y = 90{/tex}
{tex}\Rightarrow{/tex} {tex}\frac { 9 } { 7 } ( x + y ) = 90{/tex}
{tex}\Rightarrow{/tex}  {tex}x + y=70{/tex} ....................................(ii)
Solving equations (i) and (ii), we get
{tex}x = 40\ and\ y =30{/tex}.
Hence, speed of car X is {tex}40\ km/hr{/tex} and speed of car y is {tex}30\ km/hr.{/tex}