The cat Pythagoras is causing problems in the backyard. He has dug a hole with a capacity to hold 100 gallons of water. Initially, it is only half full of water that is clean. Initially, it is only half full of water that is clean. But he has three garden hoses filling the hole. The first supplies this hole at a rate of 1 gallon per minute, the second at 2 gallons per minute, and the third at 3 gallons per minute. The first two hoses supply clean water to the hole, but the third hose contains 0.2 grams/gal. of a feline contaminant. Without him seeing me, I installed a pump to help empty the hole, but it pumps only 4 gallons per minute. Write and solve a differential equation that mathematically models how much of this feline contaminant that is in this hole up to the time it fills.