SOLUTION: On a 135-mile bicycle ride, Sara averaged 5 miles per hour slower during the last 75 miles than for the first 60 miles. The entire trip lasted 8 hours. Find her rate for the firs

Question 475858: On a 135-mile bicycle ride, Sara averaged 5 miles per hour slower during the last 75 miles than for the first 60 miles. The entire trip lasted 8 hours. Find her rate for the first 60 miles.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
first part 60 miles
second part 75 miles

speed in first part x mph
speed second part x -5 mph
Total rowing time 8 hours
Time first part 60 / x
Time second part 75 / ( x -5 )

Time first part + time second part = 8 hours

60/x + 75/(x-5)= 8
LCD = x* (x -5 )
multiply the equation by the LCD
we get
60*((x-5)+75 x= 8
60x-300 +75x=8x^2-40 x
175x-300=8X^2
8 X^2 -175 x 300 = 0
8 X^2+ -175 x+ 300 =
/ 8
1 X^2 -21.88 x 37.5 =

Find the roots of the equation by quadratic formula

a= 1 b= -21.88 c= 37.5

b^2-4ac= 478.52 - -150
b^2-4ac= 328.52
= 18.13

x1=( 21.88 + 18.13 )/ 2
x1= 20 20 L= 90 20
x2=( 21.88 -18.13 ) / 2
x2= 1.88 1 7/8
Ignore x2
x = 20 mph
CHECK
Time first part + Time second part
3 + 5 = 8
m.ananth@hotmail.ca

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