Train a and B are 2823 miles apart they travel between two s

Train a and B are 2823 miles apart. they travel between two stations at an average speed of 172 miles per hour. A train leaves 2.25 hours after a train leaves station B. How long after the train leaves Station A will the trains reach the same point?

Solution

Let t=time after Train A leaves until the are at the same point
distance(d)=rate(r) times time(t) or d=rt; r=d/t and t=d/r
When train A leaves, train B has already travelled 172*2.25 or 387 mi
Now when the distance train A travels plus the distance train B travels equals 2823 mi the two trains will be at the same point
Distance train B travels =387+172t
Distance train A travels 172t
So our equation to solve is:
387+172t+172t=2823 subtract 387 from both sides
387-387+344t=2823-387 combine like terms
344t=2436 divide both sides by 344
t=7.081************* hrs--------time after Train A leaves until the are at the same point
Ck
172*7.081*********+172*7.081**********+387=2823
1218+1218+387=2823
2823=2823