SOLUTION: During the first part of a trip a canoeist travels 59 miles at a certain speed. The canoeist travels 25 miles on the second part of the trip at a speed of 5mph slower. The total ti

Algebra ->  Length-and-distance -> SOLUTION: During the first part of a trip a canoeist travels 59 miles at a certain speed. The canoeist travels 25 miles on the second part of the trip at a speed of 5mph slower. The total ti      Log On


   

Question 466400: During the first part of a trip a canoeist travels 59 miles at a certain speed. The canoeist travels 25 miles on the second part of the trip at a speed of 5mph slower. The total time for the trip was 5 hour. 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 59 miles
second part 25 miles

speed in first part x mph
speed second part x -5 mph
Total rowing time 5 hours
Time first part 59 / x
Time second part 25 / ( x -5 )

Time first part + time second part = 5 hours
59/x+25 /(x-5)= 5
LCD = x*(x-5)
multiply the equation by the LCD
we get
59*(x-5)+25x= 5
59x-295 +25x=5x^2-25x
84x-295=5X^2
5x^2-84x+295= 0
5x^2-84x+295=0
/ 5
x^2-16.8x+59=0

Find the roots of the equation by quadratic formula
a= 1 b= 10 c= -9191
b^2-4ac= 100 - 36764
b^2-4ac= 36864
sqrt%2836864%29=192
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=(-10 +192)/ 2
x1= 91
x2=( -10 -192 ) / 2
x2= -101
Ignore negative value
x=91mph First part
86 mph second part
m.ananth@hotmail.ca