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A train X starts from Meerut at 4 p.m. and reaches Ghaziabad at 5 p.m.

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A train X starts from Meerut at 4 p.m. and reaches Ghaziabad at 5 p.m.  [#permalink]

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New post 24 Apr 2011, 11:44
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A train X starts from Meerut at 4 p.m. and reaches Ghaziabad at 5 p.m.while another train Y starts from Ghaziabad at 4 p.m. and reaches Meerut at 5:30 p.m. The two trains will cross each other at:

A. 4:36 p.m.
B. 4:42 p.m.
C. 4:48 p.m.
D. 4:50 p.m.
E. 4:52 p.m.
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Re: A train X starts from Meerut at 4 p.m. and reaches Ghaziabad at 5 p.m.  [#permalink]

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New post Updated on: 24 Apr 2011, 13:34
We know that S = D/t , also D is fixed
Therefore, for train running from meerut to gazi… Sa = D / ta
but ta = 1 hr , therefore Sa = D
Now, for train running from Gazi… to meerut … Sb = D / tb
But tb = 1 ½ hr = 3/2 hr Therefore, Sb = 2D/3
However, D = Sa therefore Sb = 2Sa/3

Now, to calculate the time at which the trains will meet we need to calculate relative speed
Since, the trains are moving towards each other ,
Relative speed = Sa + Sb = Sa + 2Sa/3 = 5Sa /3
Distance will be “D” because it is fixed
And therefore Time at which the trains will meet i.e t = D / (5Sa /3)
but D = Sa therefore t = Sa / (5Sa /3) = 3 / 5 Hr = 3/5 * 60 = 36min

Thus, trains will meet at 4:36

Originally posted by vyassaptarashi on 24 Apr 2011, 12:16.
Last edited by vyassaptarashi on 24 Apr 2011, 13:34, edited 1 time in total.
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Re: A train X starts from Meerut at 4 p.m. and reaches Ghaziabad at 5 p.m.  [#permalink]

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New post 24 Apr 2011, 12:35
tparanidharan wrote:
A train X starts from Meerut at 4 P.M. and reaches Ghaziabad at 5 P.M. while
another train Y starts from Ghaziabad at 4 P.M. and reaches Meerut, at 5.30 PM. At what time the two trains meet each other.
.


Sol:

Let the distance between two points be "D miles"

Speed of X = D/1= D miles/h
Speed of Y = D/1.5= 2D/3 miles/h

Suppose X meets Y after completing "x miles" traveling for \(t_x\) hours and y traveled \(t_y\) hours

\(t_x=t_y\)

\(time=\frac{Distance}{Speed}\)

\(\frac{x}{D}=\frac{3(D-x)}{2D}\)

\(2x=3(D-x)\)

\(5x=3D\)

\(x=\frac{3}{5}D\)

Now,
x travels D miles in 1 hour
To travel (3/5)D miles, it would need 3/5 hours = 36minutes.

Thus; the trains meet at 4:36PM.
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Re: A train X starts from Meerut at 4 p.m. and reaches Ghaziabad at 5 p.m.  [#permalink]

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New post 24 Apr 2011, 16:32
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tparanidharan wrote:
A train X starts from Meerut at 4 P.M. and reaches Ghaziabad at 5 P.M. while
another train Y starts from Ghaziabad at 4 P.M. and reaches Meerut, at 5.30 PM. At what time the two trains meet each other.
.


Great solutions above. Let us look at a solution without equations too.
X takes 1 hr to cover the distance that Y covers in 1.5 hrs. That is a ratio of 2:3.
So the ratio of their speeds is 3:2 since the distance they cover is the same.
Now imagine the situation when they meet. They start at 4 and meet after some time. In this time, they have covered distance in the ratio 3:2 since their speed is in the ratio 3:2.
Attachment:
Ques2.jpg
Ques2.jpg [ 3.53 KiB | Viewed 28832 times ]


Think of X now. It has covered 3/5th of the distance that it is supposed to cover to G. It needs to cover another 2/5th. So out of its 1 hr journey, it has covered 3/5th ie. 36 mins journey (because 3/5 * 60 min = 36 min)
So they met at 4:36.

Check out this detailed concept at
http://www.veritasprep.com/blog/2011/03 ... of-ratios/
http://www.veritasprep.com/blog/2011/03 ... os-in-tsd/
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A train X starts from Meerut at 4 p.m. and reaches Ghaziabad at 5 p.m.  [#permalink]

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New post 08 May 2011, 04:59
Going to explain how I calculated it.

The first train travels the entire distance in 1 hour. The other train travels only 2/3 of the distance in one hour. When the trains meet they will together have covered the entire distance, from each others ends. The speeds of the trains are 1 times the distance per hours and 2/3 of the distance per hour. After traveling at their respective speeds for time X both trains will together have covered the entire distance.

Therefore:

1X + (2/3)X = 1.

(5/3)X = 1

X = 1/(5/3)

X = 3/5

Both trains will meet after 3/5 hours, as they will have covered the entire distance together at this point in time. 1/5 of an hour is 12 minutes. 12 x 3 is 36. The trains will meet at 4:36.
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Re: A train X starts from Meerut at 4 p.m. and reaches Ghaziabad at 5 p.m.  [#permalink]

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Re: A train X starts from Meerut at 4 p.m. and reaches Ghaziabad at 5 p.m.   [#permalink] 23 Dec 2018, 12:43
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