SOLUTION: Please help me solve this problem: Suppose it took you 30 minutes less to drive the 40 miles back home after dinner at your parent's house than it did for you to arrive there in r

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Question 875628: Please help me solve this problem:
Suppose it took you 30 minutes less to drive the 40 miles back home after dinner at your parent's house than it did for you to arrive there in rush-hour traffic. You drove about 15 mph faster on the way home. How fast did you drive each way?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
going speed x
returning speed x + 15

Distance = same 40 miles 0.5
original time – time with increased speed = 0.5 hour
t=d/t
40 / x - 40 / ( x + 10 ) = 0.5
LCD= x ( x + 15 )
multiply by LCD
40 ( x + 15 ) - 40 x = 0.5 x ( x + 15 )
40 x + 600 - 40 x = 0.5 X^2 + 7.5 x
600 = 0.5 X^2 + 7.5 x
0.5 X^2 + 7.5 x - -600 = 0
Find roots of the quadratic equation
a= 0.5 b= 7.5 c= -600

x1= ( -7.5 + sqrt( 56.25 - 1200 )) / 1
x1=( -7.5 + 35.44 )/ 1
x1= 27.94

x2= ( -7 - sqrt( 49 - 20 ) / 2
x2=( -7.5 - 35.44 )/ 1
x2= -42.94
ignore negative
going speed was 27.94 mph
add 15 for returning speed