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# My girlfriend leaves Berlin with destination Hamburg at the

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Director
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My girlfriend leaves Berlin with destination Hamburg at the [#permalink]

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26 Jan 2006, 03:14
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My girlfriend leaves Berlin with destination Hamburg at the same time I leave Hamburg with destination Berlin and our trains are driving a parallel track with the same length. After our trains pass each other at time X my girlfriend takes 1 hour to reach Hamburg with a train driving 240 km/h and I need 4 hours to reach Berlin. How fast is my train driving?

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Manager
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26 Jan 2006, 10:59
interesting exercise! any OA

My trial

240(X+1)/X+4

IF i am correct I will explain
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best regards

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Senior Manager
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26 Jan 2006, 11:16
I actually found a number, 120 km/h, calculations are lengthy though
so I suspect of my answer...

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Director
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26 Jan 2006, 12:03
Actually the solution is a number, the X is just for confusion

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Director
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26 Jan 2006, 12:42

g= girlfriend
m= me

Speed of g / speed of m = sqrt(time taken by m after passing X) / sqrt( time taken by g after passing X)

= sqrt(4) / sqrt(1)

= 2/1

So "g" is twice as fast as "m"

m= 120 km/h

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Manager
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26 Jan 2006, 14:25

Thanks

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CEO
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26 Jan 2006, 15:30
B|-------x km ---------------|-------240 km----------| H

Speed of Girl's train = 240 km/h that of boy = y

Then 240/x = x/240 i.e x*y = 240 * 240

and x/4 = y

Solve these two equations for y, we get y = 120
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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Senior Manager
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26 Jan 2006, 15:51
I think its a pretty straightforward problem. GF takes 1 hr to reach H and BF takes 4 hrs to reach B. So speed of BF's train is 1/4th of speed of GF's train. => the speed of BF's train is 240/4 = 60 km/h.

- Vipin

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Director
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27 Jan 2006, 01:40
Riuscita wrote:

Thanks

Why exactly sqrt of the respective times, don't know. But here's another fast way, if you feel reluctant with the formula.

1) the ratio of the respective speeds is X+4 : X+1 or 1 : X+1/X+4

2) g has made 240*X km's at time X; m takes 4 hours to cover the distance already traveled by g: 240X/4

So the ratio of speed and distance is

240 : 240X/4 : 1 : X+1/X+4, or, because you have to make the units equally

1 : X/4 : 1 : X+1/X+4

So,

X/4=X+1/X+4

Solve for X

XÂ² + 4X = 4X + 4

X = +- 2, -2 is out because there is no negative time

Plug in

240*2/4=120

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Manager
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27 Jan 2006, 03:35
[quote="ps_dahiya"]B|-------x km ---------------|-------240 km----------| H

Speed of Girl's train = 240 km/h that of boy = y

Then 240/x = x/240 i.e x*y = 240 * 240

and x/4 = y

Solve these two equations for y, we get y = 120[/quote]

Hey PS how do you get 240/x = y/240 and x/4 = y??

I am still stuck at 240(x+1)/x+4

The way I worked it is

total distance travelled by Girlfriend = 240x+240
total distance travelled by guy = xy+4y
I then solved for y. I dont get 120 though

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Manager
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27 Jan 2006, 08:54
Say the distance between the 2 station is Y

speed of girl's train 240
speed of boy's train S

relative speed of approach is 240 +S

since they cross after X hour so they travelled Y distance in total

so distance =speed * time
Y = (240 +S) * X ----- equation 1

also for girl distance =speed * time
Y = 240 * (x+1) ------ equation 2

for boy distance = speed * time
Y = S * (x+4) ----- equation 3

solve all the above 3 equation and u will get the answer
S =120 km/hrs
x = 2hrs
Y = 720 km

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27 Jan 2006, 08:54
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