SOLUTION: Two cars start out at the same point. One car starts out driving north at 25 mph. Two hours later the second car starts driving east at 20 mph. How long after the first car starts

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Question 242907: Two cars start out at the same point. One car starts out driving north at 25 mph. Two hours later the second car starts driving east at 20 mph. How long after the first car starts traveling does it take the two cars to be 300 miles apart?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two cars start out at the same point.
One car starts out driving north at 25 mph.
Two hours later the second car starts driving east at 20 mph.
How long after the first car starts traveling does it take the two cars to be 300 miles apart?
:
This is pythag problem; a^2 + b^2 = c^2
:
Let t = driving time of 1st car
then
25t = distance driven by the 1st car (a)
:
Let (t-2) = driving time of 2nd car
then
20(t-2) = distance driven by the 2nd car
Simplify to:
(20t-40) (b)
:
c = 300 mi
:
(25t)^2 + (20t-40)^2 = 300^2
FOIL
625t^2 + (400t^2 - 1600t + 1600) = 90000
:
625t^2 + 400t^2 - 1600t + 1600 - 90000 = 0
:
1025t^2 - 1600t - 88400 = 0
:
Simplify, divide by 25
41t^2 - 64t - 3536 = 0
:
Solve this equation using the quadratic formula; a=41; b=-64; c=-3536
:
The positive solution: x ~ 10.1 hrs after the 1st car departs