SOLUTION: During the first part of a trip, a canoeist travels 48 miles at a certain speed. The canoeist travels 5 miles on the second part of the trip at a speed 5 mph slower. The total time

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: During the first part of a trip, a canoeist travels 48 miles at a certain speed. The canoeist travels 5 miles on the second part of the trip at a speed 5 mph slower. The total time      Log On


   

Question 489600: During the first part of a trip, a canoeist travels 48 miles at a certain speed. The canoeist travels 5 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 3 hrs. What was the speed on each part of the trip? The speed on the first part of the trip was ?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
first part 48 miles
second part 5 miles

speed in first part x mph
speed second part x -5 mph
Total rowing time 3 hours
Time first part 48 / x
Time second part 5 / ( x -5 )

Time first part + time second part = 3 hours

48 / x + 5 /(x -5 ) = 3
LCD = ( x + 0 )* (x -5 )
multiply the equation by the LCD
we get
48 * (x -5 )+ 5 x = 3
48 x -240 + 5 x = 3 X^2
68 x -240 = 3 X^2
3 X^2 -68 x 240 = 0
3 X^2+ -68 x+ 240 =
/ 3
1 X^2 -22.67 x 80 =

Find the roots of the equation by quadratic formula

a= 1 b= -22.67 c= 80

b^2-4ac= 513.78 - -320
b^2-4ac= 193.78 sqrt%28%09193.78%09%29= 13.92
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=( 22.67 + 13.92 )/ 2
x1= 18.29 18 2/7
x2=( 22.67 -13.92 ) / 2
x2= 4.37 4 3/8
Ignore negative value
x = 18.29 mph speed & 5 less in the second part

CHECK
Time first part + Time second part
2.62 + 0.38 = 3