GMAT DISTANCE/RATE PRACTICE

Train A leaves Medan for Kualanamu 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 Kualanamu to medan at a constant speed. If Train B left Kualanamu at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in Medan? 

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

 ANSWER :
The diagram above incorporates the data given in the question stem.
Let x be the distance from meeting point to Kualanamu.
Speed of train A = 100 mph
Speed of train B = x/(10 min) = 6x mph (converted min to hr)
 Total time taken by both is 2 hrs.
Already accounted for is 1hr + (1/6) hr The remaining (5/6) hrs is the time needed by both together to reach their respective destinations.

 Time taken by train A to reach B + time taken by train B to reach MEDAN = 5/6 x/100 + 100/6x = 5/6 3x^2 - 250x + 5000 = 0 (Painful part of the question) x = 50, 33.33 

 (1) Train B arrived in medan before Train A arrived in Kualanamu. 

If x = 50, time taken by train A to reach B = 1/2 hr, time taken by train B to reach M = 1/3 hr If x = 33.33, time taken by train A to reach B = 1/3 hr, time taken by train B to reach M = 1/2 hr Since train B arrived first, x must be 50 and B must have arrived at 4:20.
Sufficient.
 (2) The distance between medan and kualanamu is greater than 140 miles.
 x must be 50 to make total distance more than 140. Time taken by train B must be 1/3 hr and it must have arrived at 4:20. Sufficient.

ANSWER (D)