Question 1141872
1.) A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second.

A.) 24 feet away from the wall? _____ ft/sec
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Not clear.  what's the question.
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2.) An air traffic controller spotty two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 150 miles from the point and has a speed of 300 miles per hour. The other is 200 miles from the point and has a speed of 400 miles per hour. 
A.) At what rate is the distance between the planes changing? 
Call the planes A & B.  A is going 300 mi/hr.
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A's distance from the intersection point is 150 - 300t
B's distance is 200-400t
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The distance between the at time t is the hypotenuse:
{{{h = sqrt((150-300t)^2 + (200-400t)^2)}}}
{{{h = sqrt(250000t^2 - 250000t + 62500)}}}
{{{h = 250*sqrt(4t^2 - 4t + 1)}}}
{{{h = 250*(4t^2 - 4t + 1)^0.5}}}
Differentiate wrt t
dh/dt = {{{250*(1/2)*(4t^2 - 4t + 1)^-0.5*(8t-4)}}}
dh/dt = {{{(4t^2 - 4t + 1)^-0.5*(1000t-500)}}}
dh/dt = {{{(1000t-500)/sqrt(4t^2 - 4t + 1)}}}