Question

At what speed was a train traveling on a trip when it had completed half of the total distance of the trip?
(1) The trip was 460 miles long and took 4 hours to complete.
(2) The train traveled at an average rate of 115 miles per hour on the trip.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

Answer: (E)

Statements (1) and (2) together are not sufficient.

We have to determine the speed of the train when it had completed half the total distance of the trip.

1. Given that the train travelled $460$ miles in $4$ hours, the train could have travelled at the constant rate of $115$ miles per hour for $4$ hours, and thus it could have been travelling $115$ miles per hour when it had completed half the total distance of the trip. However, the train could have travelled $150$ miles per hour for the first $2$ hours (a distance of $300$ miles) and $80$ miles per hour for the last $2$ hours (a distance of $160$ miles), and thus it could have been travelling $150$ miles per hour when it had completed half the total distance of the trip; NOT sufficient.
2. Given that the train travelled at an average rate of 115 miles per hour, each of the possibilities given in the explanation for (1) could occur, since 460 miles in 4 hours gives an average speed of $\frac{460}{4}=115$ miles per hour; NOT sufficient.

• Assuming (1) and (2), each of the possibilities given in the explanation for (1) could occur. Therefore, (1) and (2) together are not sufficient. The correct answer is E; both statements together are still not sufficient.