Question 309712
First train rate = 44 mph
in 1 hour it will have traveled 44 miles.Let the point where first train is after 1 hour be A

Let the point they meet be B

Let the distance from A to B be x miles

.
Second train rate = 52 mph
It has to travel x+44 miles to catch up with the first train
The time taken by this train to go to B  will be x+44/52
.
The first train  travels x miles in the same time as the second train takes to travel x+44 miles
..

time taken by first train to travel x miles = x/44
.
x/44 = x+44/52

52x=44(x+44)
52x=44x + 2176
8x= 2176
x=272 miles

The point they meet is x+80 miles
=272+44 miles = 316 miles
.
distance traveled by second train when ot catches up with first train = 352 mile
speed of this train = 52 mph

time taken = 316/52= 6 hours.
After 6 hours it catches up with the first train