The speed of Train A is 18 mph slower than the speed of train B. Train A travels 210 miles in the same time it takes B to travel 300 miles. Find the speed of each train.

Question

The speed of Train A is 18 mph slower than the speed of train B.  Train A travels 210 miles in the same time it takes B to travel 300 miles. Find the speed of each train.

anonymous · Answer

Let x and y be the speeds of A and B.
(x,y) is the solution to the simultaneous equations
(1) y - x = 18
(2) 210/x = 300/y

From equation (2):
300/y = 210/x = (300 - 210)/(y - x)
Plugging in the value of y - x given in (1) 
300/y = 210/x = 90/18 
300/y = 210/x = 5
Hence
Speed of train A: x = 210/5 = 42 mph
Speed of train B: y = 300/5 = 60 mph