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Two pipes, A and B can fill a tank in 24 and 35 minutes respectively. If both the pipes are opened simultaneously, after what time should A be closed so that the tank is filled in 18 minutes? Can you solve this?

the quizzer
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2 Answers2

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Hint: What faction of the tank volume does A put in per minute? What fraction does B put in per minute? B will be putting that much in for the whole $18$ minutes. How much does A have to contribute? How long does that take?

Ross Millikan
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You can make a system of equations to figure this out. Let $A(t), B(t)$ be functions that return the percentage that the tank is filled after some time $t$. You know $A(0) = B(0) = 0$ and $A(24)=B(35) = 1$. Now you are interested in finding a $t$ such that $$A(t)+B(18) = 1$$ (Assuming) that $B$ fills the tank at a constant rate, you can calculate $B(18) = \frac{18}{35}$, which means you can solve for $A(t)$ in the expression above by subtracting $\frac{18}{35}$ from each side. Assuming that $A$ also fills the tank at a constant rate, you can use a similar idea to find $t$ exactly since you have $$A(t) = \frac{17}{35} = \frac{t}{24}$$

graydad
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