Tom took 16 hours to drive the 1,000 highway miles from Chicago to Boston

When an object moves with constant speed V for a time interval t, the total distance D traveled by the object is:

D = V*t

Let Tom's initial speed be v miles per hour

The distance to traveled in the first t1 = 8 hours is:

d1 = v * t1 = 8v

Then his speed dropped by 25 mph, so now his speed is u=v-25

And the distance he traveled with this speed in t2 = 8 hours is:

d2 = u * t2 = (v-25)*8 = 8v-200

Together, the total distance Tom traveled is 1000 miles, therefore:

d1+d2 = 1000

8v + (8v-200) = 1000

16v -200 = 1000

16v = 1200

v = 1200/16 = 75mph

And in the second segment of his journey his speed was:

u = v-25 = 50 mph