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!!!!

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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) About Me  (Show Source):
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Karen travels 50 miles in t hours at r miles per hour. Carla travels 50 miles in t-48%2F60=t-4%2F5 hours at r%2B2 miles per hour.

Since d=rt, Karen's trip is described by 50=rt and Carla's trip is described by 50=%28r%2B2%29%28t-4%2F5%29

From the description of Karen's trip we can say: t=50%2Fr, so Carla's trip can be described as:

50=%28r%2B2%29%28%2850%2Fr%29-4%2F5%29
50=%28r%2B2%29%28%28250-4r%29%2F5r%29
250r=%28r%2B2%29%28250-4r%29
Apply FOIL:
250r=250r-4r%5E2%2B500-8r

Collect terms, put in standard form:
4r%5E2%2B8r-500=0

Solve the quadratic:
r%5E2%2B2r-125

Either complete the square or use the quadratic formula. You get:
r=-1+%2B-+3sqrt%2814%29. Exclude the negative root, so Karen's rate was -1+%2B+3sqrt%2814%29 mph, and Carla's was 2 mph faster or 1%2B3sqrt%2814%29 mph