Answer: the rate of the westbound train is 85 mph.
Explanation:
Let x represent the rate of the westbound train. The westbound train travels 10 miles per hour slower than the eastbound train. It means that the rate of the eastbound train is (x + 10) mph.
The two trains leave the station at the same time. The total distance covered by both trains after 3 hours is 540 miles.
Distance = speed × time
Distance covered by the westbound train in 3 hours is 3x.
Distance covered by the eastbound train in 3 hours is 3(x + 10)
Therefore,
3x + 3(x + 10) = 540
3x + 3x + 30 = 540
6x = 540 - 30 = 510
x = 510/6 = 85 mph