two trains are at stations that are 800 miles apart. if they start traveling toward each other at the same time one averaging 67 mph and the other averaging 53 mph in how many hours will they pass each other?

Answer 1

Let's hope they are on separate tracks.

let distance covered by faster train be x miles
then distance covered by slower train is 800-x

When they pass each other, their times must be the same, so ...
x/67 = (800-x)/53
53x = 53600 - 67x
120x = 53600
x = 446 2/3 miles

time = 446 2/3 / 67 = 6 2/3 hours or 6 hrs and 40 minutes