Two trains and straight line movement

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Homework Help Overview

The problem involves two trains traveling towards each other from points A and B, with specific timings and speeds provided. The first train travels for one hour, while the second train departs later and has a known average speed. The goal is to determine the distance between points A and B based on their meeting point.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between distance, speed, and time, with one suggesting to define the distance as a variable. There is an exploration of how the timings of the trains affect their meeting point and the calculations involved in determining the distance.

Discussion Status

The discussion has progressed with participants sharing their reasoning and calculations. Some guidance has been offered, and there is an indication that the original poster is attempting to verify their solution through logical steps. Multiple interpretations of the problem setup are being explored.

Contextual Notes

There is a focus on the assumptions regarding the consistency of the trains' speeds and the timing of their departures. The original poster expresses uncertainty about the initial steps in solving the problem.

mmoadi
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Homework Statement



The train travels from place A to place B for one hour. Forty minutes after the departure, first train meets with second train, which departed from place B ten minutes after first train, and it’s traveling with an average speed of 40 km / h.

Homework Equations



What is the distance between points A and B? Assuming that the movement of trains at all times can be described as consistent evenly.

The Attempt at a Solution



I really need some help because I don not know where to start.
 
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Welcome to PF!

Hi mmoadi! Welcome to PF! :wink:

Start by calling the distance x km … then the speed of the first train is x km/hour.

Show us what you get. :smile:
 
I know that the it takes for the first train to travel the distance between A and B in 1 hour.
Does this mean that the v1 (velocity of the first train) is v1= d/t which gives us that the v1 = d after I plug in the time which is 1 hour?
I also know that the two trains meet after the first train has traveled for 40 min (t1) and that the average speed of the second train is 40 km/h (v2).
So, in my opinion the whole distance is s= v1t1 + v2t2. Am I right?
So how do I continue?
 
I did some more thinking.
So, I know that the speed(v1) of the first train is v1=d. And the two trains meet after 40 min(2/3h) and the second train leaves 10 min after the first train, so does this mean that it travels for 40min-10min=30 min (1/2h) before it meets the first train. If I am right than it comes to:
s= v1t1 + v2t2 = d(2/3h) + 40km/h(1/2h)= 2/3d + 20km
d - 2/3d = 20 km
d(1-2/3) = 20 km
1/3d=20 km
d= 60 km

Is my solution right?
 
:biggrin: Woohoo! :biggrin:

Yes, that's exactly the way to do it …

and we can always check the answer (which I did :wink:) by putting 60 back into the original question, and confirming that it works! :smile:
 

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