Question 69676

Let x=Ella's rate on the freeway
Then x+10=her rate on the side roads

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

Time it takes to drive 40 mi on side roads={{{40/(x+10)}}}

Time it takes to drive 15 mi on freeway ={{{15/x}}}

Now we are told that the above times are equal, so our equation to solve is:

{{{40/(x+10)=15/x}}}  multiply both sides by x(x+10):

{{{40x=15(x+10)}}}} get rid of parens

{{{40x=15x+150}}}  subtract 15x from both sides

{{{25x=150}}}  divide both sides by x

{{{x=6 mph}}}-------------------rate on freeway

{{{x+10=6+10=16 mph}}}------------------rate on the side roads


CK

d=rt

15=6t; t=2.5 hr

40=16t; t=2.5 hr


Hope this helps---ptaylor