Question 100093
Let t=amount of time it takes second train to catch up with the first after the second train leaves at 9:00pm
time the second train catches up with the first=9:00pm+t

distance(d)=rate(r) times time(t) or d=rt;t=d/r and r=d/t

When the second train leaves, the first train has already travelled 80*3 or 240 mi


Distance first train travels =240+80t

Distance second train travels=100t

Now we know that the second train will have caught up with the first when the distance the second train travels equals the distance the first train travels.  So our equation to solve is:

100t=240+80t  subtract 80t from both sides
100t-80t=240  collect like terms
20t=240  divide both sides by 20
t=12 hrs------amount of time it takes the second train to catch up
time the second train catches up =9:00pm + 12 hrs=9:00am the next day

CK

80*12+240=100*12
1200=1200

Hope this helps---ptaylor