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
DISTANCE RATE TIME
Side roads 40 x+9
Freeway 20 x
The times are equal so now we have
=
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.