Answer
$22$ miles per hour
Not realistic at all
Work Step by Step
The function modeling the driving time is:
$$T(x)=\dfrac{470}{x+70}+\dfrac{250}{x+65}.$$
On the graph of the function we draw the line $y=8$ and find the intersection point with the function's graph:
$$(21.8,8).$$
So about $22$ miles per hour over the speed limits would be necessary in order to drive for $8$ hours. This is a very substantial amount over the speed limits which is difficult and dangerous to accomplish (due to safety and fines).
