Trains A and B travel at the same constant rate in opposite

Question

Trains A and B travel at the same constant rate in opposite directions along the same route between Town G and Town H. If, after traveling for 2 hours, Train A passes Train B, how long does it take Train B to travel the entire distance between Town G and Town H?

(1) Train B started traveling between Town G and Town H 1 hour after Train A started traveling between Town H and Town G.

(2) Train B travels at the rate of 150 miles per hour.

blueseas · Accepted Answer

just note: A and B have same speed. 
 train A travelled for 2 hours before they met.

statement 1:
train B Started 1 hour late therefore first he travelled for 1 hour before both train met.
now since both train have same speed then it means train B will also take 2 hours to complete remaining distance...hence total time = 2+1 =3 hrs
hence sufficient.

(2) Train B travels at the rate of 150 miles per hour.
now we dont know whether both train started together or anyone started late.
hence insufficient.

hence A

KarishmaB · Answer

G _____________________________ H
A --->....................................<---B

After 2 hrs of A's traveling and 1 hr of B's traveling:

G______________________________ H
 ---------------------------- AB-----------

A took 2 hrs to cover the red dotted line distance as given in the question. B will also take 2 hrs to cover this distance. Hence total time taken by B will be 1 + 2 = 3 hrs

zerosleep · Answer

Hi,
For option 2, why cant we assume both trains started simultaneouly since the question would then be -
Trains A and B travel at the same constant rate in opposite directions along the same route between Town G and Town H. If, after traveling for 2 hours, Train A passes Train B, how long does it take Train B to travel the entire distance between Town G and Town H? 
Train B travels at the rate of 150 miles per hour.

If this comes in PS - w ecould have solved this easily by saying both the trains travelled for 2 hrs with speed 150m/h. Hence the toal distance will be 150*2 + 150*2 = 600; or train B took 4 hrs.. Or simply Train A and B travelled for 2 hrs each, so 4 hours. 
I am confused why cant we do this way..?

semwal · Answer

i agree with zerosleep.
since the statement two or the question stem does not mention whether the two trains started simultaneously or at different timings, cant we presume they started together?

blueseas · Answer

hi semwal.

until and unless it is not specifically stated in the argument that they have not started at same time you cant assume so.
moreover in such cases most of the time you will get hint from one of the statement as in this case in statement 1 it clearly says that both have not started at same time.
never assume anything.
this is GMAT ..it will not confuse you in such things...so never assume anything.

hope it helps

mbhussain · Answer

logic driven question hardly any calculation involved. 
the key is "same constant speed" in the question stem, once deciphered everything should fall apart. Make a grid to get a more visual understanding

B can be rejected out rightly. A is the answer.

nayanprateek · Answer

Doesn't this statement assume that A traveled for 2 hours starting from one of the towns?

ligerdave · Answer

without a and b, we know either train can cover the whole route in 4hours. hate this kinda questions... hehe

hellosanthosh2k2 · Answer

Hi Karishma,

I initially answered E, misunderstood the statement "Trains A and B travel at the same constant rate" in the question, I assumed that A and B travel at their same constant speeds, but they could travel at diff speed but still maintain their respective speed constant. can this statement mean so?. This kind of wordings confuses me.

Yes if Speed of A and B is same, then answer is A.

KarishmaB · Answer

Note that we are talking about a single constant rate:
"Trains A and B travel at the same constant rate..."

So they must have the same rate. Else they would be travelling at their own constant rates.

GyMrAT · Answer

Lets say the speed of the two trains is = a miles per hour,

the distance between the two towns as D miles.

Since the two trains travel in opposite direction, their relative speed = a + a = 2a miles per hour

Total time of travel till they pass each other = 2 hours & we are asked to find time taken for train B to travel the whole distance = D/a

Statement 1:
Train B started traveling between Town G and Town H 1 hour after Train A started traveling between Town H and Town G

Hence we have train A traveled alone for 1 hour, covering distance = a * 1 = a miles

Distance left to travel = (D - a) miles

After 1 hour both trains are traveling towards each other & meet each other after 1 hour,

Hence we have, (D - a) = 2a * 1 = 2a

D = 3a or D/a = 3

Hence Statement 1 alone is Sufficient.

Statement 2:

Train B travels at the rate of 150 miles per hour.

Hence a = 150 miles per hour, but no information about the distance traveled.

Statement 2 alone is Not Sufficient.

Answer A.

Thanks,
GyM

prabsahi · Answer

Its a logic driven question with very less calculation..

Most important thing :A and B travel at constant speed.

Now if A travels 2 hours and B travels 1 hour to cover the distance where they meet..
implies it will take another 2 hours to cover the distance that A has covered since they are travelling at constant speeds.

So option A is sufficient.

Logic tested:If you know the proportion of time between two entities and you know they travel at same speed then irrespective of the distance(provided its constant ) you can calculate the total time taken by any of them.

Option B:

We do not know for how long B travels.

This doesnt give as wit any idea at what point of distance the two meet each other so even if we know the speed of B.We cant decide what is the time taken by B.

UnnatiSachdeva · Answer

I had a doubt.

Why can’t we take the relative speed formula for the second point -

Time taken to meet is 2 = D (which is same) / sum of speeds (300)

So with this also we get the answer.

Please clarify why it won’t be D?

Since it is asking the total time (how long) does it take for Train B to travel the entire distance?

Posted from my mobile device

Basshead · Answer

I find the best way to visualize this is to draw a line. Then we can see quickly that statement (1) is sufficient)

For statement 2 we don't know when each train started traveling. Insufficient.

Answer is A.

Pranjal3107 · Answer

ScottTargetTestPrep 
 can you please explain this one ? I am getting confused. 
D-a is the remaining distance to be covered and Relative speed is 2a
D-a=2a*t 
D-a/2a=t + 1 should be the total time B takes shouldn't it ? Please explain where I am going wrong.

ScottTargetTestPrep · Answer

Solution:

Let's make sure that I understand your terminology. You are representing the distance between the two towns as D miles and representing the speed of each train as a miles/hour. Then, the distance between the two trains when train B starts traveling is indeed D - a, and since the two trains are traveling toward each other, it will indeed take (D - a)/2a hours for the two trains to meet. However, that won't help us much since we are already told that the two trains meet 1 hour after train B starts traveling.

Instead of that, you should observe that when the two trains met, train A had been traveling for two hours, so it traveled a total of 2 * a = 2a miles. Likewise, train B had been traveling for one hour when the two trains met, so it traveled 1 * a = a miles. Since the total distance is the sum of the distances traveled by trains A and B, we can represent D as D = 2a + a = 3a. Now, we can calculate the time for train B to travel the entire distance by D/a = 3a/a = 3 hours. That's why statement one alone is sufficient to answer the question.

bumpbot · Answer

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Trains A and B travel at the same constant rate in opposite

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