A leprechaun is using a semicircular rainbow to travel from its house to a pot of gold which is 100 km apart

Question

A leprechaun is using a semicircular rainbow to travel from its house to a pot of gold which is 100 km apart. At one point in the journey, it noticed that its distance from the pot of gold is decreasing at a rate of 2 km/min. How fast is the distance of the leprechaun from the house changing if it is only 60 km away from the pot at that point?

Answer 1

Let the distance from the house to the leprechaun be u and the distance from the leprechaun to the gold be v. Then u² + v² =10000. Take the derivative and get udu/dt + vdv/dt =0 Now dv/dt =-2km/min. When v=60 km u=80 km. Therefore 80du/dt - 120 =0 and du/dt = 1.5 km/min.