SOLUTION: Help...spent two nights on these and cannot solve. A) During the first part of a trip, a canoeist travels 63 miles at a certain speed. The canoeist travels 10 miles on the second

Question 466674: Help...spent two nights on these and cannot solve.
A) During the first part of a trip, a canoeist travels 63 miles at a certain speed. The canoeist travels 10 miles on the second part of a trip at a speed of 5 mph slower. The total time for the trip is 4 hours. What was the speed on each part of the trip?
B) Write a quadratic equation having the given numbers as a solution; -6,-2.
C) Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form ax^2+bx+c=0; -sqrt 5, 3 sqrt 5.
Thank you so much for your help!!!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A) During the first part of a trip, a canoeist travels 63 miles at a certain speed. The canoeist travels 10 miles on the second part of a trip at a speed of 5 mph slower. The total time for the trip is 4 hours. What was the speed on each part of the trip?
r = the "certain speed"
t = d/r = 63/r + 10/(r-5) = 4
Multiply thru by r*(r-5)
63(r-5) + 10r = 4r(r-5) = 4r^2 - 20r
63r-315 + 10r = 4r^2 - 20r

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=3609 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 19.1343691479378, 4.11563085206221. Here's your graph:

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r = x
Ignore the answer that's less than 5.
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B) Write a quadratic equation having the given numbers as a solution; -6,-2.
(x+6)*(x+2) = 0

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C) Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form ax^2+bx+c=0; -sqrt 5, 3 sqrt 5.

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