SOLUTION: During the first part of a trip a canoeist travels 45 miles at a certain speed. The canoeist travels 10 miles on the second part of the trip at a speed of 5 mph slower. The total t

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Question 560057: During the first part of a trip a canoeist travels 45 miles at a certain speed. The canoeist travels 10 miles on the second part of the trip at a speed of 5 mph slower. The total time for the trip is 2 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 speed = x mph -- 45 miles
second part -x-5 mph ------10 miles
time first part + time second part = 2 hours
t=d/r
45/x + 10/(x-5)= 2
LCD = x(x-5)
45(x-5)+10x=2x(x-5)
45x-225+10x=2x^2-10x
2x^2-65x+225=0
Find the roots of the equation by quadratic formula

a= 2 b= -65 c= 225

b^2-4ac= 4225 - -1800
b^2-4ac= 2425 sqrt%28%092425%09%29= 49.24
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=( 65 + 49.24 )/ 4
x1= 28.56
x2=( 65 -49.24 ) / 4
x2= 3.94
first part speed = 28.56 mph
second part = 28.56-5= 23.56 mph
m.ananth@hotmail.ca