SOLUTION: Two botas starts at the same point. One sail due east starting 10 A.M. at a constant rate of 20 kph. The other sail due south starting 11 A.M. at constant rate of 9 kph. How fast a

Question 1082937: Two botas starts at the same point. One sail due east starting 10 A.M. at a constant rate of 20 kph. The other sail due south starting 11 A.M. at constant rate of 9 kph. How fast are they separating at noon?

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
The distance between them is the hypotenuse of a right triangle who's legs are measured by the rate of each boat.

Let's measure time starting at 11 AM,

So then,

So at noon, ,

So now to find the rate of separation, implicitly differentiate the equation above with respect to time.

Substituting,

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