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Question

The number of gallons of coffee a mathematician drinks on any given day is inversely proportional to how much sleep he gets the night before. On Monday, he got 9 hours of sleep and drank 2 gallons of coffee. On Tuesday, he got 6 hours of sleep. How many gallons of coffee did he drink?

Accepted Answer

Let h be the amount of sleep the mathematician gets and g be the number of gallons of coffee he drinks. Since g and h are inversely proportional, that means that gh=k for some constant k. From what we know about Monday, we can conclude that k=92=18. Consequently, for Tuesday we have 6g=18, so g=3.