SOLUTION: A and B are riding bicycles on perpendicular roads. Suppose that A is 9 km from the intersection and riding toward it at 20 kph, and B is 7 km from it and riding away from it at 25

Question 788852: A and B are riding bicycles on perpendicular roads. Suppose that A is 9 km from the intersection and riding toward it at 20 kph, and B is 7 km from it and riding away from it at 25 kph. After how many hours will they be 13 km arart?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A and B are riding bicycles on perpendicular roads. Suppose that A is 9 km from the intersection and riding toward it at 20 kph, and B is 7 km from it and riding away from it at 25 kph. After how many hours will they be 13 km arart?
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A = A's distance from the intersection
A = 9 - 20t km (t in hours)
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B = 7 + 25t
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The distance between them is the hypotenuse of the right triangle.

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=160000 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.2, -0.190243902439024. Here's your graph:

==============
Ignore the negative result.
t = 0.2 hours

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