hazelnut01 wrote:Train A leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?
(A)Â Â 8:15 am
(B) Â 8:45 am
(C)Â Â 9:00 am
(D)Â Â 9:30 am
(E) Â Cannot be determined from the information given
Distance traveled by A in 3/4 hour from 7am to 7:45am = rt = (80)(3/4) = 60 miles.
Remaining distance between A and B = (total distance) - (distance travel by A) = 210-60 = 150 miles.
When A and B travel toward each other, they WORK TOGETHER to cover the 150 miles between them, so we ADD THEIR RATES.
Combined rate for A and B = 80+70 = 150mph.
At a combined rate of 150mph, the time for A and B to cover the remaining 150 miles between them = (remaining distance)/(combined rate) = 150/150 = 1 hour.
Since they start traveling toward each other at 7:45am and meet 1 hour later, the time when they pass each other = 7:45 + 1 = 8:45am.
The correct answer is
B.
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