If a freight train and an express train leave town 390km apa

If a freight train and an express train leave town 390km apart, traveling towards one another. The freight train travels 30km slower than the express train they pass one another 3hours later. What are their speeds?

Solution

distance(d) equals rate(r) times time(t) or d=rt; t=d/r and r=d/t
Let r=speed of express
Then r-30=speed of freight train
distance express travels=speed of express times 3 hours=3r
distance freight train travels=speed of freight train times 3 hours=(r-30)*3
Now we know that as they pass the distance express has traveled plus the distance the freight train has traveled equals 390km. So our equation to solve is:
3r+3(r-30)=390 get rid of parens
3r+3r-90=390 add 90 to both sides
3r+3r-90+90=390+90 collect like terms
6r=480 divide both sides by 6
r=80km/hr--------------------------speed of express
r-30=80-30=50km/hr---------------------speed of freight train
CK
3*80+3*50=390
240+150=390
390=390