To calculate your question, we need to do the following.
Lauren ran for 45 minutes.
We first calculate what percentage/fraction 45 minutes is of 60 minutes:
45/60 = 3/4
45 minutes is 3/4 of one hour
We also know she traveled 3 miles in only 45 minutes. Now we have to calculate how much she would travel in the remaining 15 minutes.
What we simply do is calculate the speed = distance/time:
The 3 miles / (3/4) h = 4 miles
This then tells us tthat she would travel 4 miles per hour.