Bhairav runs a 15-mile race at 28 miles per hour, while Daniel runs at 15 miles per hour and Tristan runs at 10 miles per hour. What is the greatest length of time, in [i]minutes[/i], between consecutive runners' finishes?

[i]2016 CCA Math Bonanza Lightning #2.1[/i]
1. **Calculate the time taken by each runner to complete the race:**
   - Bhairav runs at 28 miles per hour.
     \[
     \text{Time for Bhairav} = \frac{15 \text{ miles}}{28 \text{ miles per hour}} = \frac{15}{28} \text{ hours}
     \]
     Converting this to minutes:
     \[
     \frac{15}{28} \text{ hours} \times 60 \text{ minutes per hour} = \frac{15 \times 60}{28} \text{ minutes} = \frac{900}{28} \text{ minutes} = \frac{225}{7} \text{ minutes}
     \]

   - Daniel runs at 15 miles per hour.
     \[
     \text{Time for Daniel} = \frac{15 \text{ miles}}{15 \text{ miles per hour}} = 1 \text{ hour}
     \]
     Converting this to minutes:
     \[
     1 \text{ hour} \times 60 \text{ minutes per hour} = 60 \text{ minutes}
     \]

   - Tristan runs at 10 miles per hour.
     \[
     \text{Time for Tristan} = \frac{15 \text{ miles}}{10 \text{ miles per hour}} = 1.5 \text{ hours}
     \]
     Converting this to minutes:
     \[
     1.5 \text{ hours} \times 60 \text{ minutes per hour} = 90 \text{ minutes}
     \]

2. **Calculate the time differences between consecutive runners' finishes:**
   - Time difference between Bhairav and Daniel:
     \[
     \text{Time difference} = 60 \text{ minutes} - \frac{225}{7} \text{ minutes} = \frac{420}{7} \text{ minutes} - \frac{225}{7} \text{ minutes} = \frac{195}{7} \text{ minutes} \approx 27.857 \text{ minutes}
     \]

   - Time difference between Daniel and Tristan:
     \[
     \text{Time difference} = 90 \text{ minutes} - 60 \text{ minutes} = 30 \text{ minutes}
     \]

3. **Determine the greatest length of time between consecutive runners' finishes:**
   - Comparing the two time differences:
     \[
     \frac{195}{7} \text{ minutes} \approx 27.857 \text{ minutes} \quad \text{and} \quad 30 \text{ minutes}
     \]
     The greatest length of time is \(30\) minutes.

The final answer is \(\boxed{30}\) minutes.