When the fast train arrives at B, the slow train has covered 6/7 of the distance. So, when they travel for the same amount of time, the slow train travels 6/7 as far as the fast train, which is another way of saying that the slow train's speed is 6/7 of the fast train's speed.
If we call the total distance between the two cities "D", when the fast train has covered 2/3 of that distance, so 2D/3 miles, the slow train will only go 6/7 as far, because its speed is 6/7 of the fast train's, so the slow train will cover (6/7)(2D/3) = 4D/7 miles. But we also know that in this time, the slow train covers D - 180 miles (all but 180 miles of the total distance). So
4D/7 = D - 180
180 = 3D/7
D = 60*7 = 420
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