Question 100026
distance(d)=rate(r) times time(t) or d=rt;t=d/r and r=d/t

Let r=rate (speed) of the first train
Then r+5=rate of the other

Distance first train travels in 2 hours =r*2 or 2r

Distance other train travels in 2 hours=(r+5)*2 or 2(r+5)

Now we know that the distance the first train travels (2r) plus the distance the other train travels (2(r+5)) equals 340-30 or 310 mi.  So our equation to solve is:

2r+2(r+5)=310 mi get rid of parens

2r+2r+10=310  subtract 10 from both sides

2r+2r+10-10=310-10 collect like terms

4r=300  divide both sides by 4

r=75 mph---------------------------speed of first train

r+5=75+5= 80 mph---------------------speed of other train

CK

75*2+80*2=310
150+160=310
310=310


Hope this helps---ptaylor