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?

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) (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

RELATED QUESTIONS
Carla can ride her bike 2 mph faster than Karen. It takes Carla 48 minutes less to travel (answered by solver91311)

Carla can ride her bike 2 mph faster than Karen. It takes Carla 48 minutes less to travel (answered by scott8148)

Andrea can rake her Dad's yard in 45 minutes. Andrea's brother Bradford rakes one and... (answered by ptaylor,nerdybill,Alan3354)

A taxi company charges $3 per ride plus $1.50 for each mile traveled. Andrea wants to... (answered by ikleyn,josgarithmetic)

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)

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)

Mary lives 6 miles from the mall. She rides her bike to the mall. She rides 4 miles... (answered by ankor@dixie-net.com)