A"local" train leaves a station and runs at an average rate of 35 mph. an hour and a half later an "express" train leaves the station and travels at an average rate of 56 mph on a parallel track. how many hours after the express train starts will the it overtake the local?

Recall your d = rt, distance = rate * time.

so...Local say "L" is going at a speed of 35mph...ok... and Express or "X" is going at 56mph.

by the time the two trains meet, and X is ready to overtake L, the distance that both have travelled, since is a parallel road, is the same, say "d".  So if L has travelled "d" miles, then X had travelled "d" miles too, over the same road, maybe different lane.

now, because X left 1 1/2 hour later, by the time they meet, say X has been running for "t" hours, but because it left 1 1/2 hour later, L has been running for " t + 1 1/2 " hours, or " t + 3/2 " hours.



so, they met 2 and a half hours later after X left, and a milllisecond later X overtook L.

They are somewhat similar