SOLUTION: During rush hour, Adriana can drive 40 miles using the side roads in the same time that it takes to travel 20 miles on the freeway. If Adriana's rate on the side roads is 9mi/h fas

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: During rush hour, Adriana can drive 40 miles using the side roads in the same time that it takes to travel 20 miles on the freeway. If Adriana's rate on the side roads is 9mi/h fas      Log On


   

Question 86024: During rush hour, Adriana can drive 40 miles using the side roads in the same time that it takes to travel 20 miles on the freeway. If Adriana's rate on the side roads is 9mi/h faster than her rate on the freeway, find her rate on the side roads.
To keep it short, my answer is 11. Am I right?
Found 2 solutions by scott8148, Edwin McCravy:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
If Adriana can travel twice as far in the same time, she must be going twice as fast.
If 9 mph faster is twice as fast, then the freeway rate must be 9 mph and the side road rate is 18 mph.
Not sure how you got 11 ...

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
During rush hour, Adriana can drive 40 miles using the side roads in the same time that it takes to travel 20 miles on the freeway. If Adriana's rate on the side roads is 9mi/h faster than her rate on the freeway, find her rate on the side roads.
To keep it short, my answer is 11. Am I right?

No, it's 18 mph.  You can think out the answer without algebra.  She can go
twice as fasr on the side roads as on the freeway, and the only way "twice as
fast" can be "9 mph faster" is for the slower rate to be 9 mph and the faster
rate to be 18 mph. 

But here's the algebraic way:

Make this chart:

             DISTANCE       RATE     TIME
Side roads                                          

Freeway                                         


Fill in the distances:

             DISTANCE       RATE     TIME
Side roads     40                                   

Freeway        20                               

Let the rate on the Freeway be x.  Then the rate on the
side roads is x+9. Fill those in

             DISTANCE       RATE     TIME
Side roads     40           x+9                   

Freeway        20            x                   

Now fill in the times by using TIME+=+%28DISTANCE%29%2F%28RATE%29


             DISTANCE       RATE     TIME
Side roads     40           x+9     40%2F%28x%2B9%29
Freeway        20            x       20%2Fx


The times are equal so now we have

              40%2F%28x%2B9%29 = 20%2Fx

Can you solve that? If not post again asking how.

Solution:  x = 9, that is 9 mph on the freeway and 18 mph
on the side roads.