I have NO IDEA on how to tackle the following problem. This question has stumped me for like...2 hours now...and I don't know what to do...

If someone could please show me a step by step on solving it, please post!

Problem:
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Two people stand back to back next to the rails in a small railway station. As the head of the express train (which does not stop at this station) reaches them, they start to walk in opposite directions parallel to the rails. As the tail of the train reaches each of them, they stop, having walked 30m and 40m respectively. If they both walked with identical, constant speeds and the train's speed was constant, how long was the train?

Answer:
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240m

This stumped me, too. It's not an easy problem. Here's what I turned up on google...

"When the tail of the train reaches the first person, both have walked 30m. Now the second person walks another 10m. During that time the tail of the train travels the 70m between the two persons' endpoints. So the train is seven times faster than each person.

When the tail of the train reaches the second person, the head of the train is 7*40m (seven times faster than the second person!) away from the point where the two persons started. The tail is 40m away from this point - in the same direction. So the train is 240m long."

What the heck....how do you know the train is seven times faster than each person?

To solve this problem, we need to analyze the situation and use the given information to find a solution. Here's a step-by-step breakdown of how to solve it:

Step 1: Understand the Problem
Read the problem carefully and identify the key information provided. In this case, we have two people walking in opposite directions parallel to the rails, with one person walking 30m and the other person walking 40m.

Step 2: Draw a Diagram
Visualize the scenario by drawing a diagram. You can draw two people standing back to back next to the rails and mark the distances they've walked.

Step 3: Identify Variables
Assign variables to the unknowns in the problem. In this case, let's consider the length of the train as our unknown. You can use the variable "x" to represent the length of the train.

Step 4: Analyze the Situation
Consider the time it takes for each person to walk their respective distances. Since both people start and stop walking at the same time, we can assume that they walk for the same amount of time.

Step 5: Use Speed = Distance/Time
Since the speed of both people is constant, we can use the formula Speed = Distance/Time. We can set up two equations using this formula:

Person 1: Speed = Distance/Time = 30m/T
Person 2: Speed = Distance/Time = 40m/T

Since they walk for the same amount of time, we can set the two equations equal to each other:

30m/T = 40m/T

Step 6: Solve for Time
Cross-multiply the equation to solve for the time:
30m * T = 40m * T

Simplifying the equation gives us:
30m = 40m

Dividing both sides by 10 gives us:
3 = 4

Step 7: Consider the Contradiction
Since the equation 3 = 4 is a contradiction, it means that there is no solution for time. However, the contradiction comes from assuming that the train is finite in length.

Step 8: Determine the Length of the Train
Since there is no solution for time, it implies that the train must be infinitely long. However, this is not realistic. So, we can conclude that the train's length is not infinite, but rather, it must have a finite length.

Step 9: Final Answer
Since the train cannot be infinitely long, the only logical answer is that the train's length is equal to the combined distances walked by the two people. Therefore, the length of the train is 30m + 40m = 70m.