Question 1095787
{{{f}}}= speed of the faster car, in km/h
{{{s}}}= speed of the slower car, in km/h
{{{system(f+s=70/1,f-s=70/7)}}} {{{system(f+s=70,f-s=10)}}}



{{{f-s=10}}}  {{{f=s+10}}}


{{{system(f+s=70,f=s+10)}}} {{{s+10+s=70}}}


{{{2s+10=70}}} {{{2s=70-10}}} {{{2s=60}}} {{{s=60/2}}} {{{s=30}}}


{{{system(s=30,f=s+10)}}} {{{highlight(system(s=30,f=40))}}}
 
EXPLANATION
When traveling towards each other,
they reduce the distance between them at a rate of {{{70km/"1 hour"}}} , so
{{{s+f=70/1}}} --> {{{s+f=70}}}
If both cars travel in the same direction,
the distance between them will change (increase or decrease)
as a rate of {{{70km/"7 hours"="10 km / h"}}} .
If the faster car was running away from the slower one,
they would bm never meet,
so if they meet in 7 hours,
the faster car is chasing the slower one.
The distance between will be decreasing at a rate of
{{{f-s=10}}} .
So, we have to solve the system
{{{system(f+s=70,f-s=10)}}} .