Question 466674
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
{{{4r^2 - 93r + 315 = 0}}}
*[invoke solve_quadratic_equation 4,-93,315]
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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
{{{x^2 + 8x + 16 = 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.
{{{(x + sqrt(5))*(x - 3sqrt(5)) = 0}}}
{{{x^2 - 2x*sqrt(5) - 15 = 0}}}