To solve this, we'll determine how many increments of $0.05$ it takes to reach $1$, and then calculate how long that would take at a rate of $0.05$ every 5 minutes.

Step-by-Step Solution

1. Determine the Number of Increments Needed to Reach 1:

   $\text{Number of increments} = \frac{1}{0.05} = 20$

   So, it takes 20 increments of $0.05$ to make 1.

2. Calculate the Time Required for Each Increment:

   Since each increment of $0.05$ takes 5 minutes:

   $\text{Total time} = 20 \times 5 = 100 \text{ minutes}$

Conclusion

It would take 100 minutes to make 1 at a rate of $0.05$ every 5 minutes.

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Would you like more details or have any questions? Here are some related questions to explore:

1. How much would you make in 1 hour at this rate?
2. If you increased the rate to $0.1$ every 5 minutes, how long would it take to make 1?
3. How long would it take to make $2$ at the same rate?
4. If the time is limited to 1 hour, how much would you make?
5. How would the total time change if each increment took 4 minutes instead of 5?

Tip: Breaking down a problem step-by-step can help you understand how different variables interact with each other.