Calculate the average speed of an express train that takes six minutes to travel three and one-half miles.

To find the average speed of the express train, you can use the formula for average speed, which is total distance traveled divided by the total time taken.

In this case, the train travels a distance of three and a half miles (which is equivalent to 3.5 miles) in a time of six minutes. First, it is important to convert the time into hours since speed is typically expressed in miles per hour (MPH). There are 60 minutes in an hour, so six minutes can be converted to hours by dividing six by 60. This gives:

[ 6 \text{ minutes} = \frac{6}{60} \text{ hours} = 0.1 \text{ hours} ]

Now, apply the average speed formula:

[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{3.5 \text{ miles}}{0.1 \text{ hours}} = 35 \text{ MPH} ]

Thus, the average speed of the express train is 35 miles per hour. This calculation directly leads us to the correct answer, confirming that the express train is indeed traveling at an average speed of