# Optimization Train Problem

1. Jun 15, 2008

### Delber

1. The problem statement, all variables and given/known data
A train leaves the station at 10:00 and travels due south at a speed of 60 km/h. Another train has been heading due west at 45 km/h and reaches the same station at 11:00. At what time were the two trains closest together?

2. Relevant equations
$$c^{2}=a^{2}+b^{2}$$

3. The attempt at a solution
The trouble I am having is the wording of the question. I think it means the trains left from two different stations and will arrive at the same time together at one station. So the equation for that scenario is:

$$f(t) = \sqrt{(60-60t)^{2}+(45t)^{2}}$$

However I get a range outside the limit of one hour. I think I'm just confused about he wording if someone can clarify it for me. Any help is appreciated.

2. Jun 15, 2008

### tiny-tim

Hi Delber!

It means train 2 arrives at the same station one hour after train 1 left.

3. Jun 15, 2008

### Delber

Thanks for the clarification.

So the new equation should be:

$$f(t)=\sqrt{(45-45t)^{2}+(60t)^{2}}$$?

Edit: Yep, I get the correct answer in the book. Thanks for the help.

Last edited: Jun 15, 2008