6. Tim the beaver is standing on the north (unforested) bank of a river. He would like to cross the river to the forested side to harvest a tree for

his dam home. The river is 100 meters wide, and Tim's d amis in the middle of the river 500 meters downstream. Suppose Tim can swim 4 kilometers per hour while pulling a tree and 8 kilometers per hour without a tree. (a) Suppose Tim swims to the opposite shore x meters downstream to harvest a tree. He swims in astraight line from his current position to the tree and then in a straight line from the tree to hisdam. Find the total distance Tim travels to get the tree and bring it to his dam as a function ofx. (b) Find the total time Tim travels as a function of x.

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