M01-34

Official Solution:


Train A departs from Keleti station in Budapest at 5:00 PM and heads towards Moscow at a constant speed of 50 mph. Train B also leaves Keleti station for Moscow later on the same day with its own constant speed. If the distance between the cities is 970 miles, at what time will Train B catch up to Train A?

(1) Train B departs from Keleti station at 6:00 PM.

From this statement, we know that when Train B starts traveling, Train A has already covered 50 miles. However, we don't have any information about the speed of Train B. Not sufficient.

(2) Train A travels at \(\frac{5}{6}\) the speed of Train B.

This statement implies that the speed of Train B is \(50*\frac{6}{5}=60\) mph. However, we still don't know the departure time of Train B. Not sufficient.

(1)+(2) We know that Train A is 50 miles ahead of Train B when Train B departs at 6:00 PM. We also know that Train B's speed is 60 mph. To catch up to the 50-mile lead, Train B will need \(\frac{50}{60-50} = 5\) hours. Therefore, Train B will catch up to Train A at 6:00 PM + 5 hours = 11:00 PM. Sufficient.


Answer: C