# Mathematics - Algebra

1. During the first part of a trip, a canoeist travels 97 miles at a certain speed. The canoeist travels 18 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.

2. If a pro basketball player has a vertical leap of about 35 inches, what is his time? Use the hang time function V=48 T^2

3. Write a quadratic equation in the variable x having the given number as solutions. Type the equation in standard form, ax^2+bx+c=0 Solution:5, only

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

(1) Let the speed on the first part of the trip be x mph. Then the speed on the second part is x - 5 mph

Time for the first part = distance/speed = 97/x hours

Time for the second part = 18/(x - 5) hours

Total time = 97/x + 18/(x - 5) = 3

[97(x - 5) + 18x]/{x(x - 5)} = 3

115 x - 485 = 3(x^2 - 5x)

3x^2 - 130x + 485 = 0

x = [130 +_ sqrt{(-130)^2 - 4 * 3 * 485}]/2(3)

x = [65 - sqrt 2770]/3 or x = [65 + sqrt 2770]/3

x = 4.123 or x = 39.210

Speed (First part) = 39.21 mph and Speed (Second part) = 39.21 - 5 = 34.21 mph

(2) T^2 = V/48 = 35/48 = 0.7296

T = sqrt 0.7296 = 0.854 s

(3) The quadratic equation is (x - 5)(x - 5) = 0, that is x^2 - 10x + 25 = 0.

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