What point will the metroliner catch up to the freight train?

Question

Metroliner traveling 90 mph

leaves Washing DC, 3 hours after a freight train traveling 60 mph. If they travel on parallel tracks, at what point will the metroliner catch up to the freight train?

 

Answer 1

Let the time the Metroliner leaves be time 0; and let the time of their meeting be t.

 

when they meet both trains would have covered the same distance

 

Distance = 90t (distance covered by Metroliner) = 60(t+3); (distance covered by freight train)

 

90t = 60t +180

 

30t = 180

 

t = 180/30 = 6 hours

 

Hence the metroliner will catch up on the freight train 6 hours after the Metroliner departs Washington D C or 9 hours after the departure of the freight train.

Answer 2

d = rt, and they will both have travelled the same distance.

 

90t = 60(t + 3)

90t = 60t + 180

30t = 180

t = 6

 

They will meet at 90(6) = 540 miles from the starting point.