SOLUTION: During the first part of a trip a canoeist travels 41 miles at a certain speed. the canoeist travels 8 miles on the second part of the trip at 5 mph slower. the total time for the

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Question 560968: During the first part of a trip a canoeist travels 41 miles at a certain speed. the canoeist travels 8 miles on the second part of the trip at 5 mph slower. the total time for the trip is 3 hours. what was the speed on each part of the trip?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
first part 41 miles
second part 8 miles

speed in first part xmph
speed second part x-5 mph
Total rowing time3 hours
Time first part 41/x
Time second part8/(x-5)

Time first part + time second part = 3 hours

41/x + 8/(x-5) =3
LCD = x*(x-5 )
multiply the equation by the LCD
we get
41*(x-5 )+8x=3(x(x-5))
41x-205 +8x=3X^2-15
64x-205 =3X^2
3X^2-64x+205= 0
3 X^2+ -64 x+ 205 =
Find the roots of the equation by quadratic formula
a= 3 b= -64 c= 205 b^2-4ac= 4096 - -2460
b^2-4ac= 1636
sqrt%28%091636%09%29= 40.45
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=( 64 + 40.45 )/ 6
x1= 17.41
x2=( 64 -40.45 ) / 6
x2= 3.93
Ignore negative value
x = 17.41 mph
first part speed = 17.41 mph
second part speed = 12.41 mph

m.ananth@hotmail.ca