**Question:** An enzyme-catalyzed reaction was carried out with the initial substrate concentration 1,000 times greater than the Km for that substrate. After 9 minutes, 1% of the substrate had been converted to product, and the amount of product was 12 mmol. If, in a separate experiment, one-third as much enzyme and twice as much of the substrate is combined, how long would it take for the same amount (12 mmol) of product to be formed?

**Core Concept:** The question involves enzyme kinetics, specifically how reaction rate and enzyme concentration affect substrate conversion. Understanding Michaelis-Menten kinetics, Vmax, and Km will help in solving this problem.

**Why the Correct Answer is Right:**

1. In the first reaction, the enzyme had 1000 times more substrate than the Km, meaning the reaction rate was already high due to excess substrate.
2. After 9 minutes, 1% of the substrate was converted to product, resulting in 12 mmol of product.
3. To solve this problem, we can use the enzyme kinetics formula:

V = (Vmax * [S]) / (Km + [S]

Where:
- V represents the reaction rate (in this case, the amount of product formed)
- Vmax is the maximum reaction rate
- Km is the substrate concentration at which the reaction rate is half of Vmax
- [S] represents the substrate concentration

**Why Each Wrong Answer is Incorrect:**

1. Option A: The reaction rate is too fast (12 mmol product in 9 minutes), so it would not take less time to reach the same amount of product (12 mmol).
2. Option B: Increasing substrate concentration (twice as much) will not significantly affect the reaction rate since the reaction is already at maximum capacity due to the excess substrate in the first reaction.
3. Option C: Decreasing enzyme concentration (one-third of the initial amount) would result in a slower reaction rate, but the substrate concentration remains the same, so the reaction rate isn't significantly affected.

**Clinical Pearls:**

1. Understanding Michaelis-Menten kinetics and Vmax is crucial for predicting reaction rates in enzyme-catalyzed reactions.
2. Excess substrate will lead to a faster reaction rate, while decreasing enzyme concentration or substrate concentration will slow down the reaction rate.
3. In this case, the reaction rate is already very high due to the excess substrate, so increasing substrate concentration or decreasing enzyme concentration will not significantly affect the reaction rate.

**Explanation:**

In the first reaction, the enzyme has a high substrate concentration (1000 times greater than the Km) and is already at maximum capacity. After 9 minutes, 1% of the substrate has been converted into product, which results in 12 mmol of product.

Let's use the Michaelis-Menten kinetics formula: V = (Vmax * [S]) / (Km + [S])

At this point, we can calculate the Vmax (