Rate determining step for parallel reaction?

I have always read that the rate determining step is the slowest step in a reaction (source: [Wikipedia](https://en.wikipedia.org/wiki/Rate-determining_step)).



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> In chemical kinetics, the overall rate of a reaction is often approximately determined by the slowest step, known as the rate-determining step (RDS) or rate-limiting step.
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However on this website ([source](http://www.faculty.ku.edu/~chem510/lect/l7s/l7s.html#SECTION00070000000000000000)), it says that the rate determining step for a parallel reaction is the *fastest step*. I was quite confused about this statement.


For a parallel reaction $\ce{B <- A -> C}$, where $\ce{A -> B}$ has rate constant $k\_1$ and $\ce{A -> C}$ has rate constant $k\_2$, the equations (from solving the first-order linear differential equations for A, B, and C, give: $A = A\_oe^{-(k\_1+k\_2)t}$, $B = \frac{k\_1\*A\_o}{k\_1+k\_2}\*(1-e^{-(k\_1+k\_2)\*t})$, and $C = \frac{k\_2\*A\_o}{k\_1+k\_2}\*(1-e^{-(k\_1+k\_2)\*t})$.


But I do not know how to proceed from there.




Let's suppose that $\ce{A -> C}$ is the fast step in the parallel reaction scheme. This implies that $k\_2 \gg k\_1$. Thus, $k\_1 + k\_2 \approx k\_2$, it is therefore (approximately) true to write the rate of consumption of $\ce{A}$ as $A\_0 e^{-k\_2t}$. This is what is meant by the fast reaction "controlling" rate for parallel reactions.


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