SOLUTION: On a recent trip Sarah's car traveled 20 mph faster on the first 150 miles than it did on the remaining 80 miles. The total time for the trip was 4 hours. Find the speed of the f
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Question 565327: On a recent trip Sarah's car traveled 20 mph faster on the first 150 miles than it did on the remaining 80 miles. The total time for the trip was 4 hours. Find the speed of the first part of the trip and show work. Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! Second part x x mph 80 miles
First part x+ 20 mph 150 miles
Time first part +Time second part = 4 hours
150 / (x 20 )+ 80 /x= 4
Multiply equation by the LCD (x+ 20 )x
150 x+ 80 (x+ 20 )= 4
150 x+ 80 x+ 1600 = 4 (x+ 20 )*x
150 x+ 80 x+ 1600 = 4 X^2 + 80 x
4 X^2 -150 x -1600 = 0
Find the roots of the equation by quadratic formula
a= 4 , b= -150 , c= -1600
b^2-4ac= 22500 + 25600
b^2-4ac= 48100
x1=( 150 + 219.32 )/ 8
x1= 46.16
x2=( 150 -219.32 ) / 8
x2= -8.66
Ignore negative value
= 46.16 mph speed in second part
66.16 mph in first part
