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# M03 #09 PS : Trains

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Manager
Joined: 28 Oct 2009
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Re: M03 #09 PS : Trains [#permalink]

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29 Mar 2012, 16:41
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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Manager
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Re: M03 #09 PS : Trains [#permalink]

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29 Mar 2013, 06:00
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]

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29 Mar 2013, 16:07
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]

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30 Mar 2013, 01:11
1
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Quick answ:
I also just drev à Quick diagram, working fine for tis question but not for more Advanced train questions.

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Re: M03 #09 PS : Trains [#permalink]

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31 Mar 2013, 09:29
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]

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01 Apr 2013, 00:54
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]

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01 Apr 2013, 04:22
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]

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02 Apr 2013, 23:49
(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.

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M03 #09 PS : Trains [#permalink]

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21 Nov 2016, 09:45
amitdgr wrote:
Two trains continuously travel between Washington DC and Baltimore, which is 120 miles away. They start simultaneously, train A at Washington and train B at Baltimore, and run at 30 and 90 mph respectively. The station turnaround times are negligible. What is the distance between the point where the trains meet for the first time and the point where they meet for the second time?

(A) 0
(B) 30 miles
(C) 60 miles
(D) 90 miles
(E) 120 miles

[Reveal] Spoiler: OA
B

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what is the best way to approach such problems ? I tried this way , the relative speed between the two trains is 30 + 90 = 120
Total distance between Train A and B is 120. The time taken to meet first time is = 120/120 = 1 hr.

So at the end of 1 hr. the two trains will meet. That is A would have traveled 30 miles. Again they will meet after an hour so train A would have reached 60 miles. Distance between 2 meeting points => 60-30 =30

Is the approach right ? is there a better approach to such problems ?

since the 2 bodies started moving at the same time from opposite directions therefore their first meeting they both covered d ( 120) and the individual distances covered is in proportion to their speeds and their 2nd meeting is after 2d ( 240) and the individual distances covered is in proportion to their individual speeds.

speed A/B = 1/3 thus distance covered by A is 1/4 of total distance

at the first meeting train A covered 1/4 (120) = 30 and in the 2nd meeting it covered 1/4(2*120) = 60 thus the difference between the 2 meeting points is 30

B

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M03 #09 PS : Trains   [#permalink] 21 Nov 2016, 09:45

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# M03 #09 PS : Trains

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