Distance problem

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February 1st 2008, 05:32 AM
Raj

Distance problem

Two trains, one starting at Point A and the other at Point B, travel toward one another.
Train #1 travels at 140km/h towards Point B, while Train #2 travels at 120km/h towards Point A.
If the trains begin at the same time, Point A and Point B are 285km apart, how far from Point A will the trains pass each other.

I'm not sure what to find here in order to answer the probelm, any help please:confused:
February 1st 2008, 09:25 AM
wingless

Follow these steps:

1- When will the trains pass each other? Find it, we can call this time $t$ .

2- How far will Train 1 go in time $t$ ?
February 1st 2008, 10:20 AM
janvdl

Quote:

Originally Posted by Raj

Two trains, one starting at Point A and the other at Point B, travel toward one another.
Train #1 travels at 140km/h towards Point B, while Train #2 travels at 120km/h towards Point A.
If the trains begin at the same time, Point A and Point B are 285km apart, how far from Point A will the trains pass each other.

I'm not sure what to find here in order to answer the probelm, any help please:confused:

For Train 1 we can say the following:

v = 140

For Train 2:

v = 120

We know Dist. = velocity x time

So the distance that $T_{1}$ travels is $140t$

For $T_{2}$ the distance is $120t$

There will be a certain time when $285$ km (or miles) minus the distance that $T_{1}$ has traveled is equal to the distance that $T_{2}$ has traveled.

So we can therefore say: $285 - 140t = 120t$

Solving for $t$ :

$t = \frac{57}{52}$

$Dist_{T1} = 140 \left( \frac{57}{52} \right) = 153,462$

EDIT: I'm thinking I should be studying for a physicist :D ...
February 1st 2008, 10:42 AM
wingless

Or you could say that their relative velocity is 140 + 120 = 260 km/h.

$V = \frac{x}{t}$

$t = \frac{x}{V}$

$t = \frac{285}{260} = \frac{57}{52}$

$(140)(\frac{57}{52}) \approx 153.5 \text{ km}$
February 1st 2008, 10:46 AM
janvdl

Quote:

Originally Posted by wingless

Or you could say that their relative velocity is 140 + 120 = 260 km/h.

I didn't even think it would be correct to say that... but it works out anyway. :confused:
February 1st 2008, 11:02 AM
wingless

Quote:

Originally Posted by janvdl

I didn't even think it would be correct to say that... but it works out anyway. :confused:

Why not? :p

Just try to imagine the scene. Two trains are 285 km away and they're going to each other. When you look at them while you stand outside the trains, on the ground, you see that one of them (Train 1) is going at 140 km/h and the other one is traveling at 120 km/h.

Now try to imagine it as you're in Train 1. You look at the other train and see that it's 285 km away and coming closer at 260 km/h. Now it's a simple calculation because your train is not moving but the other train does. It would pass you in 285/260 hours.

I hope that was helpful :)
February 1st 2008, 12:35 PM
Raj

Quote:

Originally Posted by wingless

Now try to imagine it as you're in Train 1. You look at the other train and see that it's 285 km away and coming closer at 260 km/h. Now it's a simple calculation because your train is not moving but the other train does. It would pass you in 285/260 hours.

I hope that was helpful :)

Thats a great way of thinking about it, thanks:)