Problem Solving

Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?

(1) Train B arrived in New York before Train A arrived in Boston.
(2) The distance between New York and Boston is greater than 140 miles.

OA: D

Let x = distance between NY and BOSTON
y = speed of train B

We know x/100 + x/y = 2
and 100 + y/6 = x (for train B to reach NY, it has to travel x distance)

Using 2 in 1, we get

y^2 - 500*y + 60000 = 0
y = 200 or 300
Correspondingly x = 150 or 800/6

Statement 1) It tells that B arrived before A. Only y=300 satisfies this.
If we choose y=200, A will arrive at 4:20 and B will arrive at 4:30
If we choose y=300, A will arrive at 4:30 and B will arrive at 4:20 .. This will hold true.

Sufficient!!!


Statement 2) It tells us that x > 140 which implies it has to be 150 and not 800/6 or 133.33

Sufficient!!!

Answer D.