When a Train Leaves Ciudad A at 8:00 AM Traveling to Ciudad B at 80 km/h, and Another Leaves Ciudad B at 9:00 AM at 120 km/h—Find the Exact Meeting Time on the 600 km Route

Traveling between two cities by train is a common scenario, but when two trains head toward each other from different starting points at different times, calculating their meeting point and time involves careful planning. This article explains step-by-step how to solve the problem: when a train leaves Ciudad A at 8:00 AM traveling at 80 km/h, and another departs Ciudad B at 9:00 AM toward Ciudad A at 120 km/h, with the cities 600 km apart, what time and location do the trains meet?

Understanding the Context

Base Information

  • Distance between Ciudad A and Ciudad B: 600 km
  • Train 1 departs Ciudad A at 8:00 AM, speed 80 km/h
  • Train 2 departs Ciudad B at 9:00 AM, speed 120 km/h

Step 1: Determine the head start distance

tren sale de la estaci n central de tren 2024

Image Gallery

tren sale de la estaci n central de tren 2024
Sol de América vs Sportivo Trinidense - Fecha 20 - Torneo Clausura | 🔸 ...
Un tren sale de una estación. | Foto Premium
Un tren sale de una estación con el número 2 en el frente. | Foto Premium
TRAMO. Un viaje hacia la ciudad del mañana - LAS MANOS EN LA MESA

Key Insights

By 9:00 AM, the first train has already traveled for 1 hour alone.
Distance covered in that hour = speed × time = 80 km/h × 1 h = 80 km

So, at 9:00 AM, the remaining distance between the two trains when Train 2 starts is:
600 km – 80 km = 520 km

Step 2: Relative speed when both trains are moving toward each other

After both trains are in motion (Train 1 from Ciudad A, Train 2 from Ciudad B), their speeds add because they’re approaching each other.

Continue Reading

Question: A sequence of five real numbers forms an arithmetic progression, and the sum of the first and fifth terms is 20. If the third term is 6, find the common difference.
Solution: Let the sequence be $ a - 2d, a - d, a, a + d, a + 2d $, where $ a $ is the third term and $ d $ is the common difference.
But were also told the third term is 6, so:

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Final Thoughts

Total relative speed = 80 km/h + 120 km/h = 200 km/h

Step 3: Calculate time to meet after 9:00 AM

Now, the trains are 520 km apart and closing the gap at 200 km/h.

Time to meet = Distance / Relative Speed
Time = 520 km / 200 km/h = 2.6 hours

Convert 0.6 hours to minutes:
0.6 × 60 = 36 minutes

So, the trains meet at 9:00 AM + 2 hours 36 minutes = 11:36 AM

Final Answer

The two trains will meet at 11:36 AM on the route between Ciudad A and Ciudad B.