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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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      Log On


   

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) About Me  (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?
-------------------
A = A's distance from the intersection
A = 9 - 20t km (t in hours)
---
B = 7 + 25t
================
The distance between them is the hypotenuse of the right triangle.
%289-20t%29%5E2+%2B+%287%2B25t%29%5E2+=+13%5E2
400t%5E2+-+360t+%2B+81+%2B+625t%5E2+%2B+350t+%2B+49+=+169
1025t%5E2+-+10t+-+39+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1025x%5E2%2B-10x%2B-39+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-10%29%5E2-4%2A1025%2A-39=160000.

Discriminant d=160000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+160000+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+160000+%29%29%2F2%5C1025+=+0.2
x%5B2%5D+=+%28-%28-10%29-sqrt%28+160000+%29%29%2F2%5C1025+=+-0.190243902439024

Quadratic expression 1025x%5E2%2B-10x%2B-39 can be factored:
1025x%5E2%2B-10x%2B-39+=+%28x-0.2%29%2A%28x--0.190243902439024%29
Again, the answer is: 0.2, -0.190243902439024. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1025%2Ax%5E2%2B-10%2Ax%2B-39+%29

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