Identical trains A and B are traveling non-stop on parallel tracks fro

Question

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

(A) 6:00PM
(B) 7:12PM
(C) 12:00AM
(D) 12:12AM
(E) 1:12AM

generis · Accepted Answer

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

Jayeshvekariya · Answer

Speed of trains
A: 55 mph
B: 66 mph
Rate at which B is reaching towards A= B-A = 11mph

Distance between A and B = 72 mins*55 miles/60 mins

Time taken by B to reach A= 72*55/60/11
=72*55/60*11
= 6 hrs.
So 6.12pm + 6 hrs= 12.12 am.
Option D is the right answer

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Arsh4MBA · Answer

By 6:12 Train A would have travelled 66 miles(55 miles in an hr and 11 miles in 12 mins) ahead.

When they meet x*66 = x*55+66;
11x= 66.

Therefore x=6.
so Time would be 6:12+6.
 Hence 12:12. Ans:D

gblessing · Answer

Just one additional thought:

If you wanted to work the problem, it is very easy to remove choices a and b before doing any calculations:

A: 6:00 pm (Train A would have moved for 1.2 hrs at 55 mph while Train B would have made no distance at all)
B: 7:12 pm (Train B would have moved just 1 hr at 66 mph while Train A would have been moving for 2.2 hrs at 55 mph)

ScottTargetTestPrep · Answer

We can let the time of train B = t. Train A left 72 minutes earlier than train B, which is 72/60 hours, and thus the time of train A = t + 72/60 = t + 6/5.

Using the formula distance = rate x time, the distance of train A is 55(t + 6/5) = 55t + 66 and distance train B is 66t.

Thus:

distance train A = distance train B

55t + 66 = 66t

66 = 11t

6 = t

So, the trains are besides each other at 6:12 p.m. + 6 hours = 12:12 a.m.

Answer: D

Archit3110 · Answer

for train A ; distance ; 55*(t+72/60) and for train B ; 66*t
55*(t+72/60)=66*t
solve for t = 6
6:12+6 ; 12:12 am
IMO D

TestPrepUnlimited · Answer

The difference in departure times are 1h 12min = 72 min = 6/5 hours. So by the time train B leaves, train A has traveled 55 miles/hour * 6/5 h = 66 miles. Then how long will it take for train B to catch up 66 miles? Train B is faster by train A by 11 mph. We can set up a work equation:

66=11*t
6=t

It will take 6 hours to catch up after the departure time of 6:12 pm, so B will catch up at 12:12 am.

Ans: D

josearchila86 · Answer

thanks i still dont understand why do we have to substract 66-55, please explain the logic behind that operation, thanks...

TestPrepUnlimited · Answer

Hi  josearchila86  ,

Train B and A are both moving with a gap of 66 miles in between, but Train B is faster than Train A by 11 mph so we may use that as the speed instead with the distance of 66 miles. Another way of looking at this is we can pretend Train A is not moving while Train B is travelling towards Train A at a speed of 11 mph, thus we are asking how long it will to close the gap of 66 miles with a speed of 11 mph.

MHIKER · Answer

Let in X hours the two trains will be beside each other. 
A traveled 72/60 hours before B starting. 
So, A traveled X+72/60 OR, X+6/5

Thus, 
55(X+6/55) = X*66
55X+66=66X
11X=66
X=6

THE ANSWER WILL BE 6:12+6=12:12 AM
ANS. D

jcerdae · Answer

Thank you so much for the great explanation!!
Finally I understand how to solve the GAP problems!

KhayatiK · Answer

is it possible to solve using the "same distance = time : speed, inversely related" concept?.

Identical trains A and B are traveling non-stop on parallel tracks fro

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