Trains

Let the point where the one traveling 10 mph be (0,0).......let the other start at (0,150)

So

!0T + 5T  = 150         where T is the total time traveled.........simplify

15T = 150                divide both sides by 15

T = 10                      They meet after 10 hours.......so  using the faster train's rate......

10(10)  = 100......      They meet at the point (0, 100)......in other words, at the point 100 miles north of where the faster train began

if a train is traveling north at 10 miles per hour and a second train is traveling south at 5 miles per hour at what point will the meet if they start 150 miles apart

Since the LCM of 5 and 10=10, therefore the two train will meet after 10 hours of travel.

North-bound train will have travelled: 10 X 10=100 miles or 2/3 of the distance, and,

South-bound train will have travelled: 10 X 5  =50 miles or 1/3 of the distance.