Question 404731
I need equations for each car going in the same direction and
equations for each car going in the opposite direction
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 A and B going in the same direction:
(1)
{{{d[A] = r[A]*t[A]}}}
{{{d[A] = r[A]*7}}}
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(2)
{{{d[B] = r[B]*t[B]}}}
{{{d[A] + 70 = r[B]*7}}}
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A and B going in opposite directions:
(3)
{{{d[C] = r[A]*t[C]}}}
{{{d[C] = r[A]*1}}}
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(4)
{{{d[E] = r[B]*t[B]}}}
{{{70 - d[C] = r[B]*1}}}
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 A and B going in the same direction:
Subtract (1) from (2)
(2) {{{d[A] + 70 = r[B]*7}}}
(1) {{{-d[A] = -r[A]*7}}}
{{{70 = 7r[B] - 7r[A]}}}
{{{- r[A] + r[B] = 10}}}
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A and B going in opposite directions:
Add (3) and (4)
(3) {{{d[C] = r[A]*1}}}
(4) {{{70 - d[C] = r[B]*1}}}
{{{ r[A] + r[B] = 70}}}
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Add the results:
{{{- r[A] + r[B] = 10}}}
{{{ r[A] + r[B] = 70}}} 
{{{2r[B] = 80}}}
{{{r[B] = 40}}}
and, since
{{{- r[A] + r[B] = 10}}}
{{{- r[A] + 40 = 10}}}
{{{r[A] = 30}}}
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The speed of A is 30 km/hr
The speed of B is 40 km/hr
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check answer:
{{{d[A] + 70 = r[B]*7}}}
{{{d[A] + 70 = 40*7}}}
{{{d[A] = 280 - 70}}}
{{{d[A] = 210}}} km
and
{{{d[B] = d[A] + 70}}}
{{{b[B] = 280}}} km
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{{{d[C] = r[A]*1}}}
{{{d[C] = 30}}}
{{{70 - d[C] = r[B]*1}}}
{{{70 - 30 = 40*1}}}
{{{40 = 40}}}
OK