SOLUTION: Jimmy drove for 80 miles in heavy traffic. He then reached the highway where he drove 260 miles at an average speed that was 25 miles per hour faster than the average speed he dro

Question 545136: Jimmy drove for 80 miles in heavy traffic. He then reached the highway where he drove 260 miles at an average speed that was 25 miles per hour faster than the average speed he drove in heavy traffic. If the total trip took 6 hours, determine his average speed in heavy traffic and on the highway.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
With traffic 80 miles
Highway 240 miles

speed in heavy traffic x mph
highway speed x+25 mph
Total time 6 hours
time in heavy traffic 80 / x
time in highway 240 /(x+25)

Time first part + time second part = 6 hours

(80/x)+(240/(x +25) = 6
LCD = x*(x +25 )
multiply the equation by the LCD
we get
80 * (x+ 25 )+ 240 x = 6
80 x+ 2000 + 240 x = 6 X^2 + 150 x
170 x+ 2000 = 6 X^2
6 X^2 -170 x -2000 = 0
6 X^2+ -170 x+ -2000 =
/ 6
1 X^2 -28.33 x -333.33 =

Find the roots of the equation by quadratic formula

a= 6 b= -170 c= -2000

b^2-4ac= 28900 - 48000
b^2-4ac= 76900 = 277.31

x1=( 170 + 277.31 )/ 12
x1= 37.28 37 2/7
x2=( 170 -277.31 ) / 12
x2= -8.94 -8 8/9
Ignore negative value
x=37.28 mph speed in Heavy traffic
speed inHighway = 25+37.28=62.28

CHECK
Time first part + Time second part
2.15 + 3.85 = 6

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