Chemical optimization problem to be solved

I got this problem from a book on mathematical modeling. I am bogged down on the solution because I believe that there has to be 'mention' of time on the right-hand side of the equation given. Any assistance is appreciated.

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A certain chemical reaction consists of the conversion of chemical X to chemical Y. The rate of conversion at any given time is given as R(t) and the equation R(t)= (1/100)xy holds, where x and y are the amounts of X and Y present at that time. Initially there are 99 units of X and 1 unit of Y present. Y arises only by the conversion from X.

(a)  How much X and Y are present when the conversion rate is the highest ?

(b)  Would the answer to (a) be different if there were initially 40 units of X ?

#Algebra

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Comments

Monty McGee - 3 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$