Answer
$75$ miles per hour
Work Step by Step
At 12 noon, the train was 100 miles from Chicago
By 2 P.M., the train was 250 miles from Chicago
The increase in distance from Chicago is:
$=250-100=150$ miles
The elapsed time from 12 noon to 2 p.m. is 2 hours.
Thus, the average rate is:
$=\dfrac{150\text{ miles}}{2 \text{ hours}}=75$ miles per hour