Two Trains Meeting

Work through one named subgoal at a time. Each step is checked deterministically against the canonical solver — no AI required to verify correctness. Get an AI explanation when you're stuck.

Step 1

The two trains are moving toward each other. What is their combined closing speed — the rate at which the gap between them shrinks?

Hint

When two objects move directly toward each other, their closing speed is the sum of their individual speeds.

Step 2

Divide the initial separation L by the closing speed to find the time t_meet when the trains are at the same position.

Step 3

Find the position x_meet where the trains meet, measured from Train A's starting point.

Solution walkthrough

The key insight here is to work in a frame where the gap is the only moving quantity. The gap starts at 1200 m. Train A eats into it at 20 m/s from one end; Train B eats into it at 10 m/s from the other. Together they close the gap at 20 + 10 = 30 m/s. Time to close: 1200 / 30 = 40 s. Now we know when they meet. To find where, substitute into either train's position equation. Train A: x = 20 × 40 = 800 m. Cross-check with Train B: x = 1200 − 10 × 40 = 800 m. Both agree, confirming the answer. The most common error is using the difference of speeds (10 m/s) instead of the sum. That mistake comes from thinking of one train as stationary — which only works in the reference frame of that train, not in the ground frame where both are moving. Setting the two position equations equal and solving the resulting linear equation is the systematic approach that avoids all sign errors.

Step-by-step solution

The two trains are moving toward each other. What is their combined closing speed — the rate at which the gap between them shrinks?

Divide the initial separation L by the closing speed to find the time t_meet when the trains are at the same position.

Find the position x_meet where the trains meet, measured from Train A's starting point.

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