Places A and B are 100 …

Let the speeds of the cars from A and B be x km/hr and y km/hr respectively.
Case I When the two cars move in the same direction:
In this case, let them meet at M after 5 hours

Then, AM = 5x km.
And, BM = 5y km.
{tex}\therefore{/tex} AM -BM = AB
{tex}\Rightarrow{/tex} 5x - 5y = 100
{tex}\Rightarrow{/tex} 5(x - y) = 100
{tex}\Rightarrow{/tex} x - y = 20 ...............(i)
Case II When the two cars move in the opposite directions:

Let one car move from A to B  and let the other move from B to A.
Let them meet at N after 1 hour.
Then, AN = x km and BN = y km.
{tex}\therefore{/tex}  AN + BN = AB
{tex}\Rightarrow{/tex} x + y = 100. ............. (ii)
Adding (i) and (ii), we get
(x - y) + ( x + y) = 100 + 20
{tex}\Rightarrow{/tex} x - y + x + y = 120
{tex}\Rightarrow{/tex} 2x = 120
{tex}\Rightarrow{/tex} x = 60.
Putting x = 60 in (ii), we get
x+ y = 100
{tex}\Rightarrow{/tex} 60 + y = 100
{tex}\Rightarrow{/tex} y= 100 - 60
{tex}\Rightarrow{/tex} y = 40.
So, x = 60 and y = 40
Hence , speed of the car from A = 60 km/hr,
and speed of the car from B = 40 km/hr