Question 73196

Let x=rate on freeway
Then (x+9)=rate on side roads

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

time to drive 35 mi using side roads={{{35/(x+9)}}}
And time to drive 30 miles using freeway={{{30/x}}}

Now we are told that the above two times are equal, so:

{{{35/(x+9)=30/x}}}  multiply both sides by {{{x(x+9)}}}
{{{35x=30(x+9)}}} get rid of parens

{{{35x=30x+270}}} subtract 30 from both sides
{{{35x-30x=30x-30x+270}}} collect like terms
{{{5x=270}}}  divide both sides by 5
{{{x=54}}} mph----------------------------------rate on freeway
{{{x+9=54+9=63}}} mph---------------------------rate on side roads

CK
t=d/r
35/63=30/54
0.55555=0.55555


Hope this helps---ptaylor