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# m11 03

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m11 03 [#permalink]  11 Mar 2012, 05:45
If a passenger sitting near the window in a train moving at 40 kmh noticed that it took 3 seconds for the oncoming train to pass by, what was the speed of the oncoming train if the length of the oncoming train was 75 meters?

A) 50 kmh
B) 52 kmh
C) 56 kmh
D) 60 kmh
E) 70 kmh

Denote the speed of the oncoming train as V . Then its speed relative to the passenger is V+40 . 75 meters in 3 seconds is the same as 25 meters in 1 second or 90 kmh. Thus, V+40 = 90 and V=50 kmh.
--------------------------------
I understand everything up to the point except how you get 90 kmh (or 25 meters in 1 second is the same as 90 kmh) as the total. Can someone please dumb-it-down?

Thank you!
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Re: m11 03 [#permalink]  11 Mar 2012, 07:11
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AS the trains are moving towards eachother , so their speeds ADD UP.

Toal speed = 90 kmph. out of this 40kmph is provided by one train. so the other train has a speed of 50kmph.
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Re: m11 03 [#permalink]  11 Mar 2012, 07:35
Hi Franz, I understand that when two objects are coming towards each other you add up the quantities but I still dont understand how 25 meters in 1 second is the same as 90 kmh"

V+40 yes understood - sorry if its an easy question but I'm just not seeing it clearly!
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Re: m11 03 [#permalink]  11 Mar 2012, 11:06
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Expert's post
LostinNY wrote:
Hi Franz, I understand that when two objects are coming towards each other you add up the quantities but I still dont understand how 25 meters in 1 second is the same as 90 kmh"

V+40 yes understood - sorry if its an easy question but I'm just not seeing it clearly!

25 meters in 1 second --> 25*3,600 meters in 1 hour (since there are 3,600 seconds in 1 hour) --> 25*3,600/1,000 kilometers in 1 hour (since there are 1,000 meters in 1 kilometer) --> 25*3,600/1,000=90 kilometers per hour.

Hope it's clear.
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Re: m11 03 [#permalink]  11 Mar 2012, 18:22
LostinNY wrote:
Hi Franz, I understand that when two objects are coming towards each other you add up the quantities but I still dont understand how 25 meters in 1 second is the same as 90 kmh"

V+40 yes understood - sorry if its an easy question but I'm just not seeing it clearly!

Okay I'm going to try to type it out in a long winded way, but hopefully it makes sense

First thing you want to do is get similar units. So..
$$\frac{75m}{3secs} *\frac{60sec}{1min} *\frac{60 mins}{1 hr} * \frac{1km}{1000m} = \frac{90km}{hr}$$

this is how i learned it in physics, its long, but its simple and helps eliminate any mistakes. All I'm doing is multiplying $$\frac{75m}{3secs}$$by 1 over and over again.

i.e. $$\frac{60sec}{1min} = 1$$

In the end the undesirable units in the numerator and denominator cancel out and you're left with km/hr... Which is what you're looking for.
Re: m11 03   [#permalink] 11 Mar 2012, 18:22
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# m11 03

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