SOLUTION: Andrea can ride her bike 2 mph faster than Ruby. It takes andrea 48 minutes less to travel 50 miles than it does Ruby. What is Andrea's rate in miles per hour?

Algebra ->  Formulas -> SOLUTION: Andrea can ride her bike 2 mph faster than Ruby. It takes andrea 48 minutes less to travel 50 miles than it does Ruby. What is Andrea's rate in miles per hour?      Log On


   

Question 1031854: Andrea can ride her bike 2 mph faster than Ruby. It takes andrea 48 minutes less to travel 50 miles than it does Ruby. What is Andrea's rate in miles per hour?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Andrea can ride her bike 2 mph faster than Ruby.
Let Ruby's rate be x
Andrea's rate = x+2
distance = 50 miles
Ruby's time - Andrea's time = 48 minutes => 4/5 hours
50/x - 50/(x+2) = 4/5

50(x+2)-50x = x(x+2)*4/5
50x +100 -50x=(x^2+2x)4/5
100 = (4x^2 +8x)/5
500 = 4x^2 +8x
4x^2+8x-500=0
/4
x^2+2x-125 =0
x^2+2x+1 = 125+1
(x+1)^2 = 126
x+1 = +/- sqrt(126)
x= 10.22 mph
Andrea's speed = 12.22 mph