SOLUTION: During rush hour, Ella can drive 40 miles using the side roads in the same time that it takes to travel 15 miles on the freeway. If Ella's rate on the side roads is 10 mi/h faster

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: During rush hour, Ella can drive 40 miles using the side roads in the same time that it takes to travel 15 miles on the freeway. If Ella's rate on the side roads is 10 mi/h faster      Log On


   

Question 69676: During rush hour, Ella can drive 40 miles using the side roads in the same time that it takes to travel 15 miles on the freeway. If Ella's rate on the side roads is 10 mi/h faster than her rate on the freeway, find her rate on the side roads.
I need help with this one, please?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

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%2F%28x%2B10%29
Time it takes to drive 15 mi on freeway =15%2Fx
Now we are told that the above times are equal, so our equation to solve is:
40%2F%28x%2B10%29=15%2Fx multiply both sides by x(x+10):
40x=15%28x%2B10%29} get rid of parens
40x=15x%2B150 subtract 15x from both sides
25x=150 divide both sides by x
x=6+mph-------------------rate on freeway
x%2B10=6%2B10=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