This is a tricky question, and I am happy to help.

If it took a bus 4 hours to get from town A to town B, what was the average speed of the bus for the trip?

Notice, we know the time, but we don't know the distance or the speed.

You know that the individual statements are not sufficient by themselves, so let's cut to the chase and consider the statements together:

(1) In the first 2 hours the bus covered 100 miles.
(2) The average speed of the bus for the first half of the distance was twice its speed for the second half.

Here's the problem --- after 2 hours, the bus went 100 miles -- that's the distance covered in half the time, but that's not necessarily half the distance --- in fact, 100 miles won't be half the distance if the bus goes slower in the second half.

The bus would have to cover the first half of the distance in 1 1/3 hours, and the second half of the distance in 2 2/3 hours, so that the time of the first half of the distance was half of the time of the second half of the distance, and so that the average speed of the first half would be double the speed of the second half. If we knew the two halves were at different constant speeds, we could set up some complicated equations to find out what that would mean if the bus went 100 mile in 2 hours. BUT, we have no guarantee that the speeds were constant in those two legs --- it may be that the stretch between 1 1/3 and 2 hr was the slowest stretch of the trip, or maybe the fastest stretch of the trip.

Suppose the bus drove 100 miles in 1 1/3 hours, then was stopped for 2/3 of a hour --- so was still at 100 miles at the end of 2 hrs --- and then drove another 100 miles in 2 hrs. That's a possible trip, with average speed = 200/4 = 50 mph.

Suppose the bus covered 60 miles in the first 1 1/3 hours, then hit the highway and covered 40 miles in only 2/3 of an hour --- finishing at 100 mi at the end of the two hours --- and then hit traffic and covered only 20 mile in the last two hours. That's a possible trip, with average speed = 120/4 = 30 mph.

Those are just two possibilities, consistent with both statements, and they give very different answers. We simply don't know. We need more information to calculate anything. As is, we can't determine anything. Answer = E

Does all that make sense? Please let me know if you have any further questions.

Mike