Question 83831

Let d=distance from city A to city B
r=rate on first trip
(r-10)=rate on second trip

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

First trip:

d=rt=r(2) or 
d=2r

Second trip:

d=(r-10)(2.5)

Since the distance travelled on the first and second trip is the same, we have:

2r=(r-10)(2.5)  get rid of parens

2r=2.5r-25  subtract 2.5r from both sides
2r-2.5r=2.5r-2.5r-25  collect like terms

-0.5r=-25  divide both sides by -0.5

r=50 mph but we know that:

d=2r or d=2*50=100 mi------------distance between city A and City B

CK

First trip:

2*50=100
100=100
and
(2.5)(40)=100
100=100


Hope this helps-----ptaylor