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# Two trains running in opposite directions cross a man standing on the

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Manager
Joined: 09 Jan 2016
Posts: 121
GPA: 3.4
WE: General Management (Human Resources)
Two trains running in opposite directions cross a man standing on the [#permalink]

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29 Nov 2017, 06:35
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Difficulty:

55% (hard)

Question Stats:

58% (01:18) correct 42% (01:48) wrong based on 66 sessions

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Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
A. 3:1
B. 1:3
C.3:2
D.2:3
E.5:3
Intern
Joined: 13 Nov 2017
Posts: 2
Re: Two trains running in opposite directions cross a man standing on the [#permalink]

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29 Nov 2017, 07:10
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this is how I did it and worked for me .. using the S=D/T rule we can get the lengths of each train (thinking of it as the distance here)
therefore, Train 1 Let X be speed and distance is then (D=T*S, 27X) and for train 2 it will be 17Y

knowing the time of them combined is 23 then their combined speed would be

S=D/T >> T=D/S .. 23=(27X+17Y)/(x+y)
27x+17y = 23 x+23y

4x=6y
X/Y = 6/4 = 3/2

C
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Re: Two trains running in opposite directions cross a man standing on the [#permalink]

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01 Dec 2017, 07:42
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Expert's post
Chemerical71 wrote:
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
A. 3:1
B. 1:3
C.3:2
D.2:3
E.5:3

We can let r = speed of train 1, s = speed of train 2, t = the length of train 1, and u = the length of train 2. Since speed x time = distance, we have:

r x 27 = t

s x 17 = u

And

(r + s) x 23 = t + u

If we add the first two equations, we have: 27r + 17s = t + u. If we simplify the third equation, we have 23r + 23s = t + u. Since both new equations are equal to t + u, we can equate them:

27r + 17s = 23r + 23s

4r = 6s

r/s = 6/4 = 3/2

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Re: Two trains running in opposite directions cross a man standing on the [#permalink]

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10 Dec 2017, 01:31
1
KUDOS
Expert's post
Chemerical71 wrote:
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
A. 3:1
B. 1:3
C.3:2
D.2:3
E.5:3

This question too can be done in weighted average method.
Ans $$\frac{t_{27}}{t_{17}}=\frac{23-17}{27-23}=\frac{3}{2}$$

C...

How?
Let the man stand at their meeting point in the beginning.
After 17 secs, train II would have crossed him and Train I would have another 10secs to go. Train II helps getting down these 10 secs to 6 secs
These 10 secs are covered in the ratio 6:4, so 3:2
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Re: Two trains running in opposite directions cross a man standing on the   [#permalink] 10 Dec 2017, 01:31
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