Problem: A train, an hour after starting, meets with an accident which detains it a half hour, after which it proceeds at of its former rate and arrives hours late. Had the accident happened miles farther along the line, it would have arrived only hours late. The length of the trip in miles was:
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the distance from the point of the accident to the end of the trip and the former rate of the train. Then the normal time for the trip, in hours, is
Considering the time for each trip, we have
and
and the trip is (miles).