Cooper prepared 18 kilograms of dough after working 3 hours. How much dough did Cooper prepare if he worked for 12 hours? Assume the relationship is directly proportional.

To determine how much dough Cooper would prepare in 12 hours, given that the amount of dough is directly proportional to the time spent working, we can set up a proportion based on the information given.

Given:
- 18 kilograms of dough in 3 hours.
- We need to find the amount of dough, \( x \), that Cooper would prepare in 12 hours.

The relationship is directly proportional, so we can set up the proportion:

\[
\frac{18 \text{ kg}}{3 \text{ hours}} = \frac{x \text{ kg}}{12 \text{ hours}}
\]

Now, solve for \( x \):

\[
x = \frac{18 \text{ kg} \times 12 \text{ hours}}{3 \text{ hours}} = \frac{216 \text{ kg} \cdot \text{ hours}}{3 \text{ hours}} = 72 \text{ kg}
\]

So, Cooper would prepare **72 kilograms** of dough if he worked for 12 hours.

Would you like more details on the calculation or have any questions? 

Here are some related questions you might find interesting:
1. How much dough would Cooper prepare if he worked for 5 hours?
2. If Cooper wanted to prepare 30 kilograms of dough, how long would he need to work?
3. What would be the amount of dough prepared in 1 hour?
4. How many hours would Cooper need to work to prepare 100 kilograms of dough?
5. If Cooper worked for 8 hours, how much dough would he prepare?
6. How much time is required to prepare 54 kilograms of dough?
7. How would the problem change if the relationship was not directly proportional?
8. Can you express the amount of dough prepared as a function of time?

**Tip:** When dealing with directly proportional relationships, remember that as one quantity increases, the other increases at the same rate.

Learn how to calculate the amount of dough Cooper prepares in 12 hours based on a direct proportional relationship. Solve the problem step-by-step with an example where Cooper prepares 18 kilograms of dough in 3 hours, and find out how much he would prepare in 12 hours.

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