SOLUTION: Gemma recently rode her bicycle to visit her friend who lives 12 miles away. On her way there, her average speed was 10 miles per hour faster than on her way home. If gemma spent a

Question 915232: Gemma recently rode her bicycle to visit her friend who lives 12 miles away. On her way there, her average speed was 10 miles per hour faster than on her way home. If gemma spent a total of 1 hour bicycling,find The two rates?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
on her way home speed x
onn her way there speed x + 10

Distance = same 12 miles 1
original time � time with increased speed = 1 hour
t=d/t
12 / x - 12 / ( x + 10 ) = 1
LCD= x ( x + 10 )
multiply by LCD
12 ( x + 10 ) - 12 x = 1 x ( x + 10 )
12 x + 120 - 12 x = 1 X^2 + 10 x
120 = 1 X^2 + 10 x
1 X^2 + 10 x - -120 = 0
Find roots of the quadratic equation
a= 1 b= 10 c= -120

x1= ( -10 + sqrt( 100 - 480 )) / 2
x1=( -10 + 24.08 )/ 2
x1= 7.04

x2= ( -7 - sqrt( 49 - 20 ) / 2
x2=( -10 - 24.08 )/ 2
x2= -17.04
17.04 m/h, and 7.14 m/h

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