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"
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