Wyatt and Kirk are both swimming across Crystal Lake. Kirk swims at a rate of 3 kilometers per hour, and Wyatt swims at a rate of 3.8 kilometers per hour. When Wyatt started, Kirk had already covered 0.2 kilometers. How long will it take Wyatt to catch up to Kirk? Simplify any fractions.

To determine how long it will take Wyatt to catch up to Kirk, we can set up the problem using their swimming rates and the distance that Kirk has already covered. 1. **Define the variables:** - Let \( t \) be the time in hours that Wyatt swims until he catches up to Kirk. - Kirk's swimming rate is 3 km/h. - Wyatt's swimming rate is 3.8 km/h. - Kirk has a head start of 0.2 km. 2. **Calculate the distances:** - The distance that Kirk swims in time \( t \) is given by: \[ \text{Distance}_{\text{Kirk}} = 3t + 0.2 \] - The distance that Wyatt swims in time \( t \) is given by: \[ \text{Distance}_{\text{Wyatt}} = 3.8t \] 3. **Set the distances equal to each other:** Since Wyatt catches up to Kirk when they have both swum the same distance, we can set the two distance equations equal to each other: \[ 3t + 0.2 = 3.8t \] 4. **Solve for \( t \):** Rearranging the equation gives: \[ 0.2 = 3.8t - 3t \] \[ 0.2 = 0.8t \] Now, divide both sides by 0.8: \[ t = \frac{0.2}{0.8} = \frac{1}{4} \] 5. **Convert to hours:** \(\frac{1}{4}\) hours is equivalent to 15 minutes. Thus, it will take Wyatt **15 minutes** to catch up to Kirk.