Train word problem

The appropriate formula is:  D  =  R · T           (distance  =  rate · time)

For the freight train:  since it is traveling at 40 mph,  rate = 40     --->     D  =  40T

  [D represents the distance that the freight train covers, T represents the time that it takes]

For the second train:  traveling at 60 mph,  rate  = 60  and since it starts two hours later,  time = T - 2  

and since it covers the same distance as the freight train, its distance is also D     --->     D  =  60(T - 2)

Since the distance are equal, set the right-hand side of thetwo equations equal to each other:

      40T  =  60(T - 2)

      40T  =  60T - 120

     -20T  =  -120

          T  =  6 hours     (this is the time for the freight train)

     T - 2  =  4 hours     (this is the time for the second train)     <--     the answer

{I hope that the trains are on separate, parallel tracks ...)

The LCM of 40 miles and 60 miles is 120 miles.

Train A will have travelled that distance in:120/40 =3 hours.

Train B will have travelled that distance in: 120/60=2 hours.

Since Train A had a head start of 2 hours, therefore:

The LCM of 3 hours and 2 hours is 6 hours:

Therefore, the two Trains will meet in 6 hours, at which time the 2 Trains will have travelled 240 miles.

Note that the faster train closes the gap on the slower train by 20 miles every hour.......so......before the faster train starts, the slower train is 2 X 40   = 80 miles ahead........so, from the time the faster train starts, it will take   80 / 20   = 4 hours to catch the slower train