<PRE><B>Question 789268</B>
A and B are riding bicycles on perpendicular roads.
 Suppose that A is 9km from the intersection and riding toward it at 20 kph, and B is 7km from it riding away from it at 25kph.
 After how many hours will they be 13km apart?
:
Let t = time for this to be true
A pythag problem a^2 + b^2 = c^2, where
a = (9-20t)
b = (7+25t)
c = 13
:
(9-20t)^2 + (7+25t)^2 = 13^2
FOIL
81 - 180t - 180t + 400t^2 + 49 + 175t + 175t + 625t^2 = 169
Combine like terms
400t^2 + 625t^2 - 360t + 350t + 81 + 49 - 169 = 0
A quadratic equation
1025t^2 - 10t - 39 = 0
Using the quadratic formula got a positive solution of
t = .2 hrs, they will be 13 km apart
:
:
See if this works
9-(.2*20) = 5 km for a
7+(.2*25) = 12 km for b
c = {{{sqrt(5^2 + 12^2)}}}
c = 13, confirms our solution
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