SOLUTION: During the first part of a trip, a canoeist travels 73 miles at a certain speed. The canoeist travels 14 miles on the second part of the trip at a speed 5mph slower. The total time

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: During the first part of a trip, a canoeist travels 73 miles at a certain speed. The canoeist travels 14 miles on the second part of the trip at a speed 5mph slower. The total time      Log On


   

Question 470798: During the first part of a trip, a canoeist travels 73 miles at a certain speed. The canoeist travels 14 miles on the second part of the trip at a speed 5mph slower. The total time for the trip is 3 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 73 miles
second part 14 miles

speed in first part x mph
speed second part x -5 mph
Total rowing time 3 hours
Time first part 73 / x
Time second part 14 / ( x -5 )

Time first part + time second part =3 hours

73/x+14/(x-5)=3
LCD =x* (x-5)
multiply the equation by the LCD
we get
73*(x-5)+14x=3
73x-365 +14x= 3X^2-15x
102x-365 =3x^2
3X^2-102 x+365 = 0
3x^2-102 x+365=0
/3
x^2-34x+ 121.67= 0

Find the roots of the equation by quadratic formula

a= 1 b= -34 c= 121.67

b^2-4ac= 1156 - -486.68
b^2-4ac= 669.32
sqrt%28%09669.32%09%29= 25.87
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 + 25.87 )/ 2
x1= 29.94
x2=( 34 -25.87 ) / 2
x2= 4.06

x = 29.94 mph first part
24.94 mph second part
m.ananth@hotmail.ca