SOLUTION: During the first part of a trip a canoeist travels 95 miles at a certain speed. The canoeist travels 22 miles on the second part of the trip at a speed of 5 mph slower. The total

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Question 474036: During the first part of a trip a canoeist travels 95 miles at a certain speed.
The canoeist travels 22 miles on the second part of the trip at a speed of 5 mph slower.
The total time for the trip is 3 hrs. What was the speed on each part of the trip?
Please provide exact answers for each part!
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
First part 95 miles
Second part 22 miles

speed in first part x mph
speed second part x-5 mph
Total rowing time 3 hours
Time first part 95/x
Time second part 22/(x-5)

Time first part + time second part = 3 hours

95/x+22/(x-5)= 3
LCD =x *(x-5)
multiply the equation by the LCD
we get
95*(x-5 )+22x = 3
95x-475 +22x=3x^2
117x-475=3x^2+475
3x^2-132x+475 = 0
3x^2-132x+475 = 0
/ 3
1x^2-44 x+158.33=0

Find the roots of the equation by quadratic formula

a= 1 b= -44 c= 158.33

b^2-4ac=1936+633.33
b^2-4ac=1302.67
sqrt%281302.67%09%29= 36.09
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=(44+36.09)/ 2
x1= 40.05
x2=(44 -36.09 ) / 2
x2= 3.95 Ignore
x = 40.05 mph first part
35.05 mph second part

m.ananth@hotmail.ca