M7MBA wrote:Train A leaves the station at 5:00, and travels north at 50 miles per hour. If train B leaves the same station some time later, heading in the same direction as train A, at what time will train B overtake train A?
(1) Train B leaves the station at 6:00.
(2) Train A travels at 5/6 the speed of train B.
Statement 1:
From 5pm to 6pm, A travels on its own for 1 hour at a rate of 50 mph, with the result that A travels ahead 50 miles.
Since B's rate is unknown, we cannot determine when B catches up to A.
INSUFFICIENT.
Statement 2:
Since A's 50-mph rate is 5/6 of B's rate, we get:
50 = (5/6)B
B = (6/5)50 = 60 mph.
Since B = 60 mph and A = 50 mph, every hour B travels 10 more miles than A, with the result that B catches up to A at a rate of 10 mph.
Since we don't know how far ahead A has traveled, we cannot determine when B catches up to A.
INSUFFICIENT.
Statements combined:
Since B is 50 miles behind A and catches up at a rate of 10 mph, the time for B to catch up = 50/10 = 5 hours.
Thus, the time at which B catches up = 6pm + 5 hours = 11pm.
SUFFICIENT.
The correct answer is
C.
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