Let
x--------> the time in hours
y-------> the distance in miles
we know that
The speed is equal to
[tex]Speed=\frac{distance}{time}[/tex]
in this problem
[tex]Speed=\frac{y}{x}[/tex]
[tex]y=(Speed)*x[/tex]
Equation First Train
[tex]y1=70x[/tex]
Equation Second Train
[tex]y2=80x[/tex]
[tex]y1+y2=600\ miles[/tex] ---------> equation [tex]1[/tex]
Substitute the values of [tex]y1[/tex] and [tex]y2[/tex] in the equation [tex]1[/tex]
[tex]70x+80x=600[/tex]
Solve for x
[tex]150x=600[/tex]
[tex]x=4\ hours[/tex]
therefore
the answer is
[tex]4\ hours[/tex]
