The problem asks how long it takes for your friend to complete 18 laps, given that you and your friend skate at the same rate, and you complete 6 laps in 5 minutes.

We can set up a proportion to solve this:

$\frac{6 \, \text{laps}}{5 \, \text{minutes}} = \frac{18 \, \text{laps}}{x \, \text{minutes}}$

Now we can solve for $x$, the time it takes your friend to complete 18 laps.

Let's solve it step-by-step:

$\frac{6}{5} = \frac{18}{x}$

Cross-multiply to get:

$6x = 5 \times 18$

Simplifying:

$6x = 90$

Now divide both sides by 6:

$x = \frac{90}{6} = 15 \, \text{minutes}$

So, it will take your friend 15 minutes to complete 18 laps.

Would you like further details or clarifications?

Here are five related questions for practice:

1. If it takes 5 minutes for 6 laps, how long would it take to complete 12 laps?
2. How many laps could you complete in 20 minutes at the same rate?
3. What is the rate in laps per minute?
4. If your friend completed 24 laps, how long would that take?
5. How many laps would your friend complete in 10 minutes?

Tip: Use proportions to solve problems involving rates and ratios, as they maintain consistency across different scales.