SOLUTION: While traveling to and from a certain destination, you realized increasing your speed by 10 mph saved 1 hours on your return. If the total distance of the roundtrip was 600 miles,

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Question 871050: While traveling to and from a certain destination, you realized increasing your speed by 10 mph saved 1 hours on your return. If the total distance of the roundtrip was 600 miles, find the speed driven while returning.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
speed to go there x
speed returning x + 10

Distance = same 300 km
original time – time with increased speed = 1 hour
t=d/t
300 / x - 300 / ( x + 10 ) = 1
LCD= x ( x + 10 )
multiply by LCD
300 ( x + 10 ) - 300 x = 1 x ( x + 10 )
300 x + 3000 - 300 x = 1 X^2 + 10 x
3000 = 1 X^2 + 10 x
1 X^2 + 10 x - -3000 = 0
Find roots of the quadratic equation
a= 1 b= 10 c= -3000

x1= ( -10 + sqrt( 100 - 12000 )) / 2
x1=( -10 + 110 )/ 2
x1= 50

x2= ( -7 - sqrt( 49 - 20 ) / 2
x2=( -10 - 110 )/ 2
x2= -60 ignore negative value
to go there speed = 50 mph
returning speed = 60 mph