Question 84758
We know that distance = speed * time. Now Let us denote the speed by s and speed by t then
600= s * t
where s is in miles per hour and t is in hours
Now Second condition says that had he gone 20mph faster, the trip would have taken 1 hour less. But the distance remains the same
so 
in the second case:
600=(s+20)(t-1)
which means if we equate the two equations, we have

st= (s+20)(t-1)
solving:
s= 20t -20

substituting the value of t from the equation 600 = st in terms of s, we have
{{{s= ((20*600)/s)-20}}}
which yields to 
{{{s^2+20*s-12000=0}}}
solving by quadratic equation method and taking the positive value only, we have
s=100 miles per hour