Xóchitl, who has already warmed up, immediately starts to pedal at a rate of \[18\,\dfrac{\text{km}}{\text{h}}\] on a 

stationary bike

.

She sees that her friend Cowessess has already pedaled \[12\] minutes at an average rate of \[10\,\dfrac{\text{km}}{\text{h}}\].

**Assuming Cowessess's rate stays the same, how long would Xóchitl have to pedal to catch up to Cowessess's distance?**

To solve this problem, we need to find out how long Xóchitl needs to pedal to cover the same distance that Cowessess has already covered. Let's break down the problem step by step.

### Step 1: Determine the distance Cowessess has already covered
Cowessess has been pedaling for 12 minutes at a rate of \(10 \, \dfrac{\text{km}}{\text{h}}\).

First, convert 12 minutes into hours:
\[
12 \, \text{minutes} = \dfrac{12}{60} \, \text{hours} = 0.2 \, \text{hours}
\]

Now, calculate the distance Cowessess has covered:
\[
\text{Distance} = \text{Rate} \times \text{Time} = 10 \, \dfrac{\text{km}}{\text{h}} \times 0.2 \, \text{hours} = 2 \, \text{km}
\]

So, Cowessess has pedaled 2 kilometers.

### Step 2: Calculate the time Xóchitl needs to cover 2 km
Xóchitl is pedaling at a rate of \(18 \, \dfrac{\text{km}}{\text{h}}\).

To find out how long it will take her to catch up, we need to determine how much time she will take to cover 2 kilometers.

Use the formula for time:
\[
\text{Time} = \dfrac{\text{Distance}}{\text{Rate}} = \dfrac{2 \, \text{km}}{18 \, \dfrac{\text{km}}{\text{h}}} = \dfrac{2}{18} \, \text{hours} = \dfrac{1}{9} \, \text{hours}
\]

Convert this time into minutes:
\[
\dfrac{1}{9} \, \text{hours} = \dfrac{1}{9} \times 60 \, \text{minutes} = \dfrac{60}{9} \, \text{minutes} \approx 6.67 \, \text{minutes}
\]

### Final Answer
Xóchitl would have to pedal for approximately **6.67 minutes** to catch up to the distance Cowessess has covered.

---

**Follow-up Questions:**

1. What would happen if Cowessess increased her speed after Xóchitl started pedaling?
2. How would the result change if Xóchitl started at a different speed?
3. What if Xóchitl had a head start instead of Cowessess?
4. How far would Xóchitl be after 10 minutes of pedaling?
5. How long would it take both of them together to pedal 20 kilometers?

**Tip:** When dealing with problems involving time and distance, it’s crucial to keep units consistent throughout the calculations to avoid errors.

Learn how to solve a distance, rate, time problem involving Xóchitl and Cowessess. Calculate how long Xóchitl needs to pedal at 18 km/h to catch up to Cowessess, who has already pedaled 2 km at 10 km/h. Includes step-by-step solution and unit conversion. Suitable for Grades 6-8.

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