When Were Two Trains Closest Together?

In summary, the question asks at what time two trains that left from different stations and traveled at different speeds will be closest together at the same station. The equation for this scenario is f(t) = √((45-45t)^2 + (60t)^2).
  • #1
Delber
19
0

Homework Statement


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?

Homework Equations


[tex]c^{2}=a^{2}+b^{2}[/tex]

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:

[tex]f(t) = \sqrt{(60-60t)^{2}+(45t)^{2}}[/tex]

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.
 
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  • #2
Delber said:

Homework Statement


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?

Hi Delber! :smile:

It means train 2 arrives at the same station one hour after train 1 left. :smile:
 
  • #3
Thanks for the clarification.

So the new equation should be:

[tex]f(t)=\sqrt{(45-45t)^{2}+(60t)^{2}}[/tex]?

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

Related to When Were Two Trains Closest Together?

1. What is the "Optimization Train Problem"?

The "Optimization Train Problem" is a mathematical optimization problem that involves finding the most efficient way to dispatch a set of trains on a given railway network. The goal is to minimize travel time and maximize the usage of the railway network while adhering to constraints such as train schedules and track capacity.

2. What are the main challenges of the Optimization Train Problem?

There are several challenges associated with the Optimization Train Problem, including the complexity of real-world railway networks, the large number of variables and constraints involved, and the need to balance conflicting objectives such as minimizing travel time and maximizing network utilization.

3. How is the Optimization Train Problem solved?

The Optimization Train Problem is typically solved using mathematical optimization techniques such as linear programming, mixed-integer programming, or heuristic algorithms. These methods use mathematical models and algorithms to find the best possible solution to the problem.

4. What are the potential applications of the Optimization Train Problem?

The Optimization Train Problem has a wide range of potential applications in the transportation industry, including optimizing train schedules for passenger and freight trains, improving the efficiency of railway networks, and reducing transportation costs. It can also be applied to other areas such as supply chain management and logistics.

5. What are the benefits of solving the Optimization Train Problem?

The successful optimization of train schedules can lead to significant benefits, such as reduced travel time, improved punctuality, increased capacity utilization, and cost savings. It can also lead to more efficient use of resources and a more sustainable transportation system.

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