If a train travels at $80 \mathrm{mph}$ for $15 \mathrm{~min}$, what is the distance traveled?

Step 1 ：Given that a train travels at a speed of 80 mph for a duration of 15 minutes, we are to find the distance it covers.

Step 2 ：We know that distance is calculated by the formula: \(\text{Distance} = \text{Speed} \times \text{Time}\)

Step 3 ：However, the speed is given in miles per hour (mph) and the time is given in minutes. Therefore, we need to convert the time from minutes to hours before we can use the formula. There are 60 minutes in an hour, so we can do this conversion by dividing the time in minutes by 60.

Step 4 ：Let's denote the speed as \(s\) and the time in minutes as \(t\). So, \(s = 80\) mph and \(t = 15\) minutes.

Step 5 ：Converting the time to hours, we get \(t_{\text{hours}} = \frac{t}{60} = \frac{15}{60} = 0.25\) hours.

Step 6 ：Substituting the values of \(s\) and \(t_{\text{hours}}\) into the distance formula, we get \(\text{Distance} = s \times t_{\text{hours}} = 80 \times 0.25 = 20\) miles.

Step 7 ：Final Answer: The distance traveled by the train is \(\boxed{20}\) miles.