+11 Car 1 is 10 miles east of car 2. Car 1 is driving at 10 mph eastward, car 2 is driving north at a speed of 20 mph. how fast is the distance changing after 2 hours of driving?
+486 It's not a glitch, it is because someone previously spammed on here, and then I flagged the post and the admin came on and took down the spam posts. There were 2 spam posts and 2 of my replies. They are still there, just only visible to the mods and the admin.
+36916 Related rates and the pythagorean theorem
x = car 1 = 2 hrs * 10 m/hr = 20 miles and dx/dt = 10 m/hr
y = car 2 = 2hrs * 20 m/hr = 40 miles and py/dt = 20 m/hr
Pythagorean theorem for the distance between the two cars :
x^2 + y^2 = s^2 s^2 = 2000 now differentiate with respect to time (using chain rule)
2x dx/dt + 2y dy/dy = 2s ds/dt We have all of these variables except ds/dt (which we are looking for) ...so plug in
2(20) * 10 + 2 (40) *20 = 2 (sqrt(2000) * ds/dt
ds/dt = 2000/(2 sqrt(2000)) = 1000/sqrt(2000) = 22.36 m/hr
