johnycute wrote:

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.

The question is very tough and it took me lot of time to solve it....

Lets first rephrase the question.

Consider for train B:

Rate=r; Time=t; Distance=d

ForTrain A:

Rate=100mph;Time=2-t;Dist=d

Now from this information we know 2 equations.

d=100(2-t) ----------------(A)

d=rt-------------------------(B)

We also know that when the trains pass each other (going in opposite directions), Train A has been traveling for 1 hour and Train B has been traveling for 10 minutes or 1/6 of an hour.

This means that Train A has traveled 100 miles and Train B has traveled r/6 miles.
Thus, the total distance from New York to Boston can be expressed using the equation

d=100+r/6------------------(C)

If we compare A and B;

t=200/100+r----------------(D)

Now compare equation B and C and put the value of "t" from equation D.

r(200/100+r) = 100 + r/6

(r-300)(r-200)=0

Thus, the rate, r, of Train B is either 300 mph or 200 mph.

If Train B has a rate of 300 mph. It travels 50 miles in 1/6 hour, at which point it meets Train A which has already traveled 100 miles. Therefore, the total distance from Boston to New York must be 150 miles. Thus, Train B's total traveling time was 1/2 hour, and Train A's total traveling time was 1 1/2 hours. Train B arrived in New York at 4:20 PM and Train A arrived in Boston at 4:30 PM.

If Train B has a rate of 200 mph. It travels 33 1/3 miles in 1/6 hour, at which point it meets Train A which has already traveled 100 miles. Therefore, the total distance from Boston to New York must be 133 1/3 miles. Thus Train B's total traveling time was 2/3 hour, and Train A's total traveling time was 1 1/3 hours. Train B arrived in New York at 4:30 PM and Train A arrived in Boston at 4:20 PM.

Statement (1) tells us that Train B arrived in New York before Train A arrived in Boston. From this, we know that Scenario 1 must have occurred and Train B arrived in New York at 4:20 PM. We have sufficient information to answer the question.

Statement (2) tells us that the distance between New York and Boston is greater than 140 miles. This means that Scenario 2 is not possible so Scenario 1 must have occurred: Train B arrived in New York at 4:20 PM. Again, we have sufficient information

to answer the question.

The correct answer is (D): Each statement ALONE is sufficient