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?
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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.
{{{(9-20t)^2 + (7+25t)^2 = 13^2}}}
{{{400t^2 - 360t + 81 + 625t^2 + 350t + 49 = 169}}}
{{{1025t^2 - 10t - 39 = 0}}}
*[invoke solve_quadratic_equation 1025,-10,-39]
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Ignore the negative result.
t = 0.2 hours