Two trains leave from points A and B towards each other. If the train from A leaves 2 hours earlier than the train from B

| January 14, 2021 | education

Two trains leave from points A and B towards each other. If the train from A leaves 2 hours earlier than the train from B, then the meeting will take place in the middle of the journey. If the trains leave at the same time, they will meet in 3 hours 45 minutes. Find train speeds and the distance between A and B if you know that the speed of one train is 40 km / h more than the speed of the other.

1. Let X km / h be the speed of the first train.
Then the speed of the second train is (X + 40) km / h.
2. Trains go towards each other.
This means the speed of convergence X + X + 40 = (2 * X + 40) km / h.
3. It is known that if the trains leave at the same time, they will meet in 3 hours 45 minutes.
3 hours 45 minutes = 3 3/4 hours = 15/4 hours.
Then the distance S = (2 * X + 40) * 15/4 km.
4. If the second train leaves 2 hours earlier, the meeting will take place in the middle of the journey.
S / 2 / X = S / 2 / (X + 40) + 2.
(X + 40) * S = X * S + 4 * X * (X + 40).
10 * S = X * X + 40 * X.
We replace from the previous equation.
(2 * X + 40) * 150/4 = X * X + 40 * X.
X * X – 35 * X – 1500 = 0.
Discriminant D = 35 * 35 + 4 * 1500 = 85 * 85.
X = (35 + 85) / 2 = 60 km / h – the speed of the first train.
60 + 40 = 100 km / h – the speed of the second.
(40 + 100) * 15/4 = 600 km – distance.
Answer: Train speeds are 60 km / h and 100 km / h, distance is 600 km.



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