Identify Given Data and Total Time Difference

Note the two speeds and the net time difference between being late and early: $\Delta t = 10 + 15 = 25 \text{ minutes} = \frac{25}{60} \text{ hours}$.

$\Delta t = 10 + 15 = 25 \text{ minutes} = \frac{5}{12} \text{ hours}$

Apply Distance Formula for Variable Speeds

Use the standard distance formula based on two speeds and time difference: $d = \frac{S_1 \times S_2}{S_2 - S_1} \times \Delta t$.

$d = \frac{S_1 \times S_2}{S_2 - S_1} \times \Delta t$

Substitute Values and Calculate Distance

Substitute $S_1 = 5$, $S_2 = 6$, and $\Delta t = \frac{5}{12}$ into the formula to find the distance: $d = \frac{5 \times 6}{6 - 5} \times \frac{5}{12}$.

$d = \frac{30}{1} \times \frac{5}{12} = 12.5 \text{ km}$