Question on Find Speed of Three Trains

Topic : Speed of Trains

Question : Three train one eastbound, one westbound and one northbound,leave the city at the same time.The speed of the northbound train is 20miles/hr greater than the speed of the eastbound train. After two hours, the distance between the westbound train and the eastbound train is 140miles. Twice the speed of the westbound train is 30miles per hour more than the speed of the northbound train, Find the speeds of the three trains.

Solution :

From the figure 2x+2y = 140--------------(1)
and 2y = x + 20 + 30
2y = x +50
2y - x = 50-------------------(2)
Consider (1) and (2)
2y + 2x = 140
2y - x = 50
----------------
+3x = 90
x = 30

and substitute the value of x in (2)
2y - x = 50
2y - 30 = 50
2y = 80
y = 40
So,

Speed of eastbound train in 30miles per hour
Speed of westbound train in 40miles per hour
Speed of Northbound train in 50miles per hour