SOLUTION: during the first part of the trip, a canoeist travels 30 miles at a certain speed. the canoeist travels 16 miles on the second part of the trip at a speed 5mph slower.t he total ti

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: during the first part of the trip, a canoeist travels 30 miles at a certain speed. the canoeist travels 16 miles on the second part of the trip at a speed 5mph slower.t he total ti      Log On


   

Question 434479: during the first part of the trip, a canoeist travels 30 miles at a certain speed. the canoeist travels 16 miles on the second part of the trip at a speed 5mph slower.t he total time for the trip is 5 hrs. 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 x mph
Second Part -5 mph

Distance first part 30 miles
Distance second part 16 miles

speed first part x mph
speed second part = x-5 mph
Total rowing time 5 hours
Time first part 30/x
Time second part 16/(x-5)
Time first part + time second part =5 hours
30/x+16 /(x-5)= 5
LCD =(x )*(x-5)
multiply the equation by the LCD
we get
30*(x-5 )+16x=5
30x-150 +16x=5X^2-25x
46x -150=5X^2-25x
5X^2-71x+150 =0
5x^2-71x+150=0
/5
X^2-14.2x+30=0
Find the roots of the equation by quadratic formula
a= 1 b= -14.2 c= 30
b^2-4ac= 201.64 - -120
b^2-4ac= 81.64 ,sqrt%28%0981.64%09%29= 9.04
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=( 14.2 + 9.04 )/ 2
x1= 11.62
x2=( 14.2 -9.04 ) / 2
x2= 2.58 This is not possible
Speed first part = 11.62 mph
Speed second part = 6.62 mph