Question: An engineer wants to test the complex and dangerous process of filling and emptying a tank of liquid hydrogen. The tank has a volume of

An engineer wants to test the complex and dangerous process of filling and emptying a tank of liquid hydrogen. The tank has a volume of 400,000 cm^3. The tank can be filled 5,000 cm^3 per hour faster than it can be emptied.

Part A

Suppose r is the rate at which this tank is filled in thousands of cubic centimeters per hour. What is the equation for t, the total number of hours it takes to fill and empty this tank, in terms of r. Simplify the expression and explain.

Part B

Use technology to graph the equation from Part A to find the fill rate that would allow you to fill and empty the tank in 100 hours. Check for extraneous solutions, and explain your work. Round to the nearest tenth.

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