Easy math puzzles
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53 members have voted
August 19th, 2026 at 6:12:07 PM
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Quote: DogHandQuote: WizardYou have a 100-gallon tub full of pure water. Someone pours two gallons of salt into it, which is immediately absorbed. Pure water flows into the tank at a rate of five gallons per minute. Meanwhile, water leaves a hole in the bottom at the same rate. How long will it take for the water to contain 0.1 gallons of salt?
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Wiz,
Here is my solution:
Dog Hand
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I have a slightly difference answer.
At time t=T min, salt=0.1 gal, water=100 gal.
At time t=x, salt=y. We have dy/dx=-5y/100; therefore, the general solution to the differential equation is
𝑦=A* exp(-x/20)=2*exp(-x/20).
Where we have used: at time t=0 min, salt=2 gal, water=100 gal. Therefore
x=-20 ln(y/2)= -20 ln (0.1/2) = 59.915 min.
