Un tren sale de la Ciudad A a las 8:00 AM y viaja hacia la Ciudad B a una velocidad constante de 80 km/h. Otro tren sale de la Ciudad B a las 9:00 AM hacia la Ciudad A a 120 km/h. Si la distancia entre las ciudades es de 600 km, ¿a qué hora se encontrarán? - Nelissen Grade advocaten
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
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
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.
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📰 إذن، أكبر عدد صحيح يجب أن يقسم حاصل ضرب أي أربعة أعداد صحيحة متتالية هو $\boxed{24}$. 📰 السؤال: ما هي أكبر قيمة ممكنة للقاسم المشترك الأكبر $(a,b)$، إذا كان مجموع عددين صحيحين موجبين $a + b = 96$؟ 📰 الحل: ليكن $d = \gcd(a, b)$. إذن $a = dx$، $b = dy$، حيث $\gcd(x, y) = 1$.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.
