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M03 #09 PS : Trains

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Re: M03 #09 PS : Trains [#permalink] New post 29 Mar 2012, 02:26
Easy question!!! :)

Train speeds: Train A 30mph, Train B 90mph. Total distance is 120 miles.
in 1st hour, train A would have travelled 30 miles, train B would have travelled 90 miles.

I st hour:
Train A
--------->
30 miles
<----------------------------- Train B
90 miles
Train A and B meet at 30 miles.

2nd hour: train A would have another travelled 30miles, train B would have travelled another 90 miles.(remaining 30 miles and 60 miles on return)

Train A
--------->------------>
60miles
----------------------> Train B
60miles
second time, they meet at 60 miles.
Difference in miles between the point they met at first time and second time is 60-30= 30 miles

So the answer is B.
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Re: M03 #09 PS : Trains [#permalink] New post 29 Mar 2012, 15:41
Is the simpler way to answer the question : t1 = 30/mph t2 =90mph

So 30+90 = 120 = 1 hour.

In one hour train 1 will have traveled 30 mi therefore they would have to meet at 30 mi.
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Re: M03 #09 PS : Trains [#permalink] New post 29 Mar 2013, 05:00
Seeing the values:
After 1 hour. The trains meet for the first time. A and B intersect at Point 1
After 1 more hour, the train with 90kmph(B) overtakes 30kmph(A) train at Point 2

(30mph)->A__________1_________2____________________B<-(90mph)
A <-30m-> 1 <-30m-> 2 <-60m-> B

Distance between 1 and 2 is 30 miles.
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Re: M03 #09 PS : Trains [#permalink] New post 29 Mar 2013, 15:07
I still cannot understand how to tackle the problem despite I read all the provided explanations . Any body can kindly provide a step -by-step explanation please?
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Re: M03 #09 PS : Trains [#permalink] New post 31 Mar 2013, 08:29
I think i took an easier approach:
The relative speed of train B will be 90+30=120
distance 120miles, relative speed for B (assuming A stationary) =120mph
time taken =120/120=1 hours

Hence they meet after one hour i.e. A has travelled 30miles and B has travelled 90 miles.

DC---30----60---90----120 Baltimore

We can say for every 30 miles A covers train B covers 90 miles..

after meeting 30miles away from DC:

DC---x---60---90---120

Train A goes till 30 miles farther where train B covers 90 kms.. i.e. reaches DC and meets at point 60 miles away from DC

Hence they meet now at:
DC---X----x---90---120

Clearly we can see distance between two meeting points is 30 miles


Hope it helps :)
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Re: M03 #09 PS : Trains [#permalink] New post 31 Mar 2013, 23:54
Ans: (B)..

Since Train A starts from Washington and Train B from Baltimore, hence they are travelling in opposite direction. So the relative speed = 120 mph (90 + 30)..
Total time taken = Total distance / Relative speed => 120 / 120 = 1hr.

So the distance travelled by each train is : A - 30 miles ; B - 90 miles. Let this point of first rendevouz be X. Now the catch in the question is that they travel continuously, so there is a possibility that they may meet again while travelling in the same direction.. figure below:
Washisngton .............X............Y........... Baltimore
30m 30m 30m

Now we can observe that while Train A would had travelled another 30 miles in next 1hr (its speed is 30 mph). So it’s distance from Washington = 60 miles.
Train B would had covered the remaining 30 miles from X till Washington and backtracked to the current position of Train A by covering remaining 60m from Washington within 1 hr (train B speed is 90mph). Let this point of second meet be Y.
So the distance between Y and X = 60 – 30 = 30 miles
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Re: M03 #09 PS : Trains [#permalink] New post 01 Apr 2013, 03:22
For distance =120 and 2 trains at 90+30 mph= 120mph makes it very easy.
For 1st time they will meet at 30miles from Washington..now from this moment we check when will they meet again, again the distance between them is 120 so again train A will meet after 30miles.
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Re: M03 #09 PS : Trains [#permalink] New post 02 Apr 2013, 22:49
(B) 30 miles

Total Rate = 90+30 = 120
Distance = 120

Time to meet the trains = 120/120 = 1 Hour..

So in every one hour both trains will meet
i.e. After 1 hour Train A reaches to a place C= 30 km from washington
After 2 hour Train A reaches to a place D= 60 km from washington, Distance Between C and D = 30
After 3 hour Train A reaches to a place E= 90 km from washington, Distance Between D and E = 30


Do let me know in case there is a hole in the logic :)

nice Question.
Re: M03 #09 PS : Trains   [#permalink] 02 Apr 2013, 22:49
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