# Distance problem

• Feb 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:
• Feb 1st 2008, 09:25 AM
wingless

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

2- How far will Train 1 go in time $\displaystyle t$ ?
• Feb 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 $\displaystyle T_{1}$ travels is $\displaystyle 140t$

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

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

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

Solving for $\displaystyle t$:

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

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

EDIT: I'm thinking I should be studying for a physicist :D ...
• Feb 1st 2008, 10:42 AM
wingless
Or you could say that their relative velocity is 140 + 120 = 260 km/h.

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

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

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

$\displaystyle (140)(\frac{57}{52}) \approx 153.5 \text{ km}$
• Feb 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:
• Feb 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 :)
• Feb 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:)