SOLUTION: Two cyclists start biking from the same location. Kate heads south at an average pace of 17 mph. An hour later, Nate heads west at an average pace of 14 mph. Which of the following

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Question 905428: Two cyclists start biking from the same location. Kate heads south at an average pace of 17 mph. An hour later, Nate heads west at an average pace of 14 mph. Which of the following could be used to determine how long after Kate starts riding it takes for them to be at least 35 miles apart? [Let t represent time.]
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!
Using Pythagorean Theorem
(17t)^2 + (14(t-1))^2 = 35mi^2
289t^2 + 196(t^2 - 2t + 1) = 1225mi
485t^2 -392t - 1029 = 0

Solved by pluggable solver: SOLVE quadratic equation with variable

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=2149924 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.91573393180164, -1.10748650912123. Here's your graph: