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 * 55 miles/hour = 66 miles

At 6:12 p.m., both trains are moving. But 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. 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. Train B catches Train A at 12:12 a.m.

Answer D