SOLUTION: Mary makes a round trip of 150 km each way. Coming back Mary was able to average 25 km per hour faster than she had going. If the total trip took three and a half hours, then what

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Question 536708: Mary makes a round trip of 150 km each way. Coming back Mary was able to average 25 km per hour faster than she had going. If the total trip took three and a half hours, then what was Mary's speed coming back?
Thank you in advance:)
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Forward speed x mph
Return speed x 25 mph
Total time 3.5 hours
Time forward 150 / x
Time return 150 / ( x 25 )

Time first part + time second part = 3.5 hours

150 / x + 150 /(x 25 ) = 3.5
LCD = x (x +25 )
multiply the equation by the LCD
we get
150 * (x 25 )+ 150 x = 3.5
150 x 3750 + 150 x = 3.5 X^2 + 87.5 x
212.5 x 3750 = 3.5 X^2
3.5 X^2 -212.5 x -3750 = 0
3.5 X^2+ -212.5 x+ -3750 =
/ 3.5
1 X^2 -60.71 x -1071.43 =

Find the roots of the equation by quadratic formula

a= 1 b= -60.71 c= -1071.43

b^2-4ac= 3686.22 - 4285.71
b^2-4ac= 7971.9sqrt%28%097971.94%09%29= 89.29
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 60.71 + 89.29 )/ 2
x1= 75
x2=( 60.71 -89.29 ) / 2
x2= -14.29 -14 2/7
Ignore negative value
x = 75 kph
Returning speed = 100 kph
m.ananth@hotmail.ca