Phew!!! Difficult one for me; took me more than 3 minutes just to formulate the equation and more than 3 minutes to solve and arrive at conclusion.

Sol:

The total time is 2 hours

"A" traveled 100 miles in 1 hour when it met train B, which by then would have traveled 10 mins or 1/6 hours.

Let's take distance traveled by B in 10 minutes or 1/6 hours to be "x" miles. So; train A travels 100 miles + x miles and B travels x miles+ 100 miles

Now; let's just talk about time

A traveled 100 miles in 1 hour

A would have traveled x miles in x/100 hour

B traveled x miles in 1/6 hour

B would have traveled 100 miles in 100/(6x) hour

Total time combined is 2; Thus;

1+ x/100 + 1/6 + 100/(6x) = 2 ---> This is the equation

Solving the above; we get

\(3x^2-100x-150x+5000=0\)

\((x-50)(3x-100)=0\)

x could be 50 miles

or

x could be 100/3 miles approx 33 miles

1.

It says B arrived at NY before A arrived at Boston.

Say x=50

B spent 10 minutes to travel x miles or 50 miles

B will spend 20 minutes to travel remaining 100 miles

A spent x/100 hour to travel x miles means; 1/2 hour

As we can see after A and B met; B traveled 20 minutes and A 30 minutes.

This satisfies the statement 1 for x=50

Let's check x=33 as well

B spent 10 minutes to travel x miles or 33 miles

B will spend approx 30 minutes to travel 3 times the distance (100=3*33), which is remaining 100 miles.

A spent x/100 hour to travel x miles means; 33/100 hour approx 1/3 hours; 20 minutes approx

As we can see after A and B met; B traveled 30 minutes and A 20 minutes.

This will make statement 1 false. Thus x can't be 33.

We found unique solution for x=50.

Thus we know; train B arrived New York 30 minutes after it started. i.e. at 4:20PM

Sufficient.

2.

This one is easy;

It says the distance > 140 miles

if x=33

Distance = 100+x = 133 <140

x=33 can't be true

if x=50

Distance = 100+x = 150 >140

x=50 is true

Sufficient.

Ans: "D"

_________________

~fluke

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