SOLUTION: During the first part of a trip, a canoeist travels 90 miles at a certain speed. The canoeist travels 12 miles on the second part of the trip at a speed 5mph slower. The total time

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: During the first part of a trip, a canoeist travels 90 miles at a certain speed. The canoeist travels 12 miles on the second part of the trip at a speed 5mph slower. The total time      Log On


   

Question 470745: During the first part of a trip, a canoeist travels 90 miles at a certain speed. The canoeist travels 12 miles on the second part of the trip at a speed 5mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip?
1.Speed of 1st part of the trip?
2.Speed of 2nd part of the trip?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
first part x mph
second part -5 mph

first part 90 miles
second part 12 miles

speed in first part x mph
speed second part x -5 mph
Total rowing time 5 hours
Time first part 90 / x
Time second part 12 / ( x -5 )

Time first part + time second part = 5 hours

90/x+12/(x-5)= 5
LCD =(x)*(x-5)
multiply the equation by the LCD
we get
90*(x-5)+12x = 5
90x-450+ 12x=5x^2-25x
127x-450 =5x^2
5X^2-127 x+450=0
5X^2-127 x+450 =0
/5
x^2-25.4 x+90=0

Find the roots of the equation by quadratic formula a= 1 b= -25.4 c= 90

b^2-4ac= 645.16-( -360)
b^2-4ac= 285.16
sqrt%28%09285.16%29= 16.89
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=( 25.4 + 16.89 )/ 2
x1= 21.14 ====> 21 1/7
x2=( 25.4 -16.89 ) / 2
x2= 4.26 ===> 4 1/4 (Ignore this value)
x = 21.14 mph LCD =speed
first part 21.94 mph
seond part 21.14-5=16.14 mph
m.ananth@hotmail.ca