+655 Eric and Harrison are standing in a field, and Eric is 400 feet directly East of Harrison. Eric starts to walk North at a rate of 4 feet per second, while Harrsion starts to walk South at the same time at a rate of 6 feet per second. After 30 seconds, at what rate is the distance between Eric and Harrison changing?
+985 We can model the rate of a change as a right triangle with base x=400 feet and height y increasing at a rate of 10 feet per second.
After 30 seconds, y=10⋅30=300
If the distance between Eric and Harrison is z, the Pythagorean Theorem gives us: z2=x2+y2.
The distance between Eric and Harrison is: x2=3002+4002⇒x=500
Differentiating both sides also yields 2z·z′=2x·x′+2y·y′. Plugging in our values, we get 2·500z′=2·400·0+2·300·10, which gives us z′=6 feet per second.
I hope this helped,
Gavin
