SOLUTION: Carla can ride her bike 2 mph faster than Karen. It takes Carla 48 minutes less to travel 50 miles than it does Karen. What is Carla's rate (mph)? HELP MUCH APPRECIATED!!!!

Question 143415This question is from textbook algebra: structure and method: book1
: Carla can ride her bike 2 mph faster than Karen. It takes Carla 48 minutes less to travel 50 miles than it does Karen. What is Carla's rate (mph)? HELP MUCH APPRECIATED!!!! This question is from textbook algebra: structure and method: book1

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Karen travels 50 miles in t hours at r miles per hour. Carla travels 50 miles in hours at miles per hour.

Since , Karen's trip is described by and Carla's trip is described by

From the description of Karen's trip we can say: , so Carla's trip can be described as:

Apply FOIL:

Collect terms, put in standard form:

Solve the quadratic:

Either complete the square or use the quadratic formula. You get:
. Exclude the negative root, so Karen's rate was mph, and Carla's was 2 mph faster or mph
RELATED QUESTIONS
Carla can ride her bike 2 mph faster than Karen. It takes Carla 48 minutes less to travel (answered by scott8148)

Andrea can ride her bike 2 mph faster than Ruby. It takes andrea 48 minutes less to... (answered by mananth)

Two sisters like to compete on their bike rides. Autumn can go 4 mph faster than her... (answered by ikleyn)

A man can ride his bike 18 miles in the same time it takes him to run 6 miles. He can... (answered by TimothyLamb,MathTherapy)

Karen can jog to work in 2/3 of an hour. When she rides her bike, it takes her 1/4 of an... (answered by ankor@dixie-net.com)

Rene can ride her bike sixty miles in one hour less time than it takes Sue to ride sixty... (answered by Paul)

tessa can ride her bike 24 miles in 1 hour less time than it takes Gary to walk 9 miles.... (answered by sudheerb)

Karen can jog to work in 4/5 of an hour. When she rides her bike, it takes her 3/10 of an (answered by ankor@dixie-net.com)

Karen and John take 3 hours to clean the house. Karen alone can clean the house 1 hour... (answered by stanbon)