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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

**Two trains 140 meters and 160 meters long run at the speeds of 60 km/hour and 40 km/hour respectively in the opposite directions on parallel tracks. Find the time in seconds which they take to cross each other.**

Let's solve this using geogebra. First we will have to represent the two trains.

1) Scale the x - axis from -100 to 300 and the y axis from 0 to 6.

2) Draw a slider called t with Min = 0 and Max = 11 and increment 0f .001, Repeat = Increasing (once).

3) Create points A,B,C,D and E anywhere on the graph in quadrant 1.

4) For A enter (11.1111111*t, 3) in its definition. For B enter (11.1111111*t + 160, 3).

5) Draw a line segment between A and B.

6) For C enter (-16.66667 t + 160, 1) in its definition. For D enter (-16.66667 t + 300, 1).

7) Draw a line segment between C and D.

8) For E enter (-16.66667 t + 300, 3).

9) Draw a vector colored red from D to E and Hide E.

10) Move the slider and you should see AB and CD moving in opposite directions and carrying the vector with them. These represent the two trains relative length and speeds.

11) Run the animation of the slider until the red arrow is directly under A and then press pause. Adjust using the shift arrow keys and eyeball the best answer. Read t or time from the slider.

12) Check the first drawing for how it should look before the run and the second one for after.What did you get? Do you agree with the algebra answer of 10.8?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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bobbym wrote:

Do you agree with the algebra answer of 10.8?

10.8 seconds? Yeah, Id say so.

Look at the problem this way. Each train is travelling at 100 km/hour relative to the other and has 300 metres to travel. So the time taken is .

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**math.guru.92****Member**- Registered: 2013-07-25
- Posts: 3

this problem can be solved using the equation:

s=vt

here s=140+160=300m

v=40+60=100km/h

first we convert velocity into meters per second

so we get v=(10*1000)/3600

now using t=s/v

we get t=10.8 seconds

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,771

Hi all;

Geogebra solutions like post #1 would be nice.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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