# Algebra

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During the first part of a trip, a canoeist travels 98 miles at a certain speed. The canoeist travels 10 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 3 hours. What was the speed on the FIRST part of the trip? What was the speed on the SECOND part of the trip?
(type an integer or a decimal. Round to the nearest hundredth)

• Algebra -

98mi @ X mi/hr.

10mi @ (x-5) mi/hr.

T = 98/x + 10/(x-5) = 3hrs.
Multiply both sides by x(x-5):
98(x-5) + 10x = 3x(x-5),
98x - 490 + 10x = 3x^2 - 15x,
-3x^2 + 108x + 15x - 490 = 0,
-3x^2 + 123x -490 = 0,
Solve using Quadratic Formula and get:
X = 36.53, and 4.47.
The required value of x is > 5.

X = 36.53 mi/hr = Speed during 1st part of trip.

X-5 = 31.53 = Speed during 2nd part of trip.

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