A farmer is transferring 800 kilograms of grain from a truck into a silo (a building for storage of grain). The silo initially contains 40 kilograms of grain. The machine used to transfer the grain does so at a constant rate, and after 15 minutes only 200 kilograms of grain remain in the truck. However, the machine is faulty and 1 out of every 10 kilograms of grain removed from the truck falls onto the ground instead of going into the silo. Let S(t) be the amount of grain in the silo and T(t) be the amount of grain in the truck (in kilograms) at time t (in minutes). (a) At what time E has the truck been emptied? (b) When the truck is empty, how much grain is in the silo and how much is on the ground? (c) Show that T(t) = 800 1 - 40t and S(t) = 40 + 36t for t€ [0, E.