+270 Two people start walking from the same point. One person travels west at a rate of 3 mph, and the other walks north at a rate of 4 mph. At what rate is the distance between the two people changing 1 hour after they start walking?
+128578 Using, the Pythagorean Theorem, the distance between them after one hour = r
r = √ [3^2 + 4^2] = 5 miles
And using the general theorem, again, we have
r^2 = x^2 + y^2 differentiating with respect to time, t, we have
2r dr/dt = 2x dx/dt + 2y dy/dt divide through by 2
r dr/dt = x dx/dt + y dy/dt
We are looking for dr/dt and x = 3miles, y = 4 miles and dx/dt = 3mph and dy/dt = 4mph
So we have
5miles [dr/dt] = 3miles *3miles per hour + 4miles per hour * 4mph
5miles [dr/dt] = 9m^2ph + 16m^2ph
5miles dr/dt = 25m^2ph divide through by 5 miles
dr/dt = 25m^2ph / 5miles
dr/dt = 5mph
