hazelnut wrote:
Identical trains A and B are traveling non-stop on parallel tracks from New York to Chicago. Train A leaves New York at 5PM and travels at a constant speed of 55mph (assume constant speed from start of trip). Train B leaves New York at 6:12PM and travels at a constant speed of 66mph (assume constant speed from start of trip). At what time will the two trains be exactly beside each other?
(A) 6:00PM
(B) 7:12PM
(C) 12:00AM
(D) 12:12AM
(E) 1:12AM
Using the gap method in a "chase" scenario.
Train A, while traveling alone, creates the distance (gap) between the trains.
Train A travels alone for \(\frac{6}{5}\) hours
(r*t) = D (gap distance)
55 miles/hour * \(\frac{6}{5}\) hrs = 66 miles
At 6:12 p.m.,
both trains are moving.
This is the time at which the distance gap begins to get closed.
Train B travels faster than train A and will overtake A.
When travelers move in the same direction, subtract slower rate from faster rate to get the rate at which the gap shrinks (relative speed).
(66 - 55) = 11 mph
How long will it take for B to catch A?
D/r = t
D is 66. Relative rate, r, is 11.
66/11 = 6 hours
The clock time at which they are "exactly beside one another" is calculated from the time B leaves, which is when
both trains are traveling and the gap begins to shrink.
Add 6 hours to 6:12 p.m., when B leaves
Train B catches Train A at 12:12 a.m.
Answer D
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