SOLUTION: During the first part of a trip, a canoeist travels 16 miles at a certain speed. The canoeist travels 3 miles on the second part of the trip at a speed 5 mph slower. The total time

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Question 805763: During the first part of a trip, a canoeist travels 16 miles at a certain speed. The canoeist travels 3 miles on the second part of the trip at a speed 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!
During the first part of a trip, a canoeist travels 16 miles at a certain speed. The canoeist travels 3 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 3 hours. What was the speed on each part of the trip?
16 miles ------- speed ----------x
3 miles----------speed-----------(x-5)
Time First part + time II part = 3
t=d/r
16/x + 3/(x-5) =3
multiply equation by x(x-3)
16(x-5)+3x=3x(x-5)
16x-80+3x =3x^2-15x
3x^2-34x+80=0
Find the roots of the equation by quadratic formula
iiiii
a= 3 , b= -34 , c= 80

b^2-4ac= 1156 + -960
b^2-4ac= 196
%09sqrt%28%09196%09%29=%0914%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=( 34 + 14 )/ 6
x1= 8.00
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 34 -14 ) / 6
x2= 3.33

canoe speed 8 mph

m.ananth@hotmail.ca