To find out how long it will take Mary to run 10 miles, we first need to determine her pace based on her performance over the 2 miles.
Mary ran 2 miles in 23 minutes. To find her pace per mile, we divide the total time by the number of miles:
\[ \text{Pace} = \frac{\text{Total Time}}{\text{Distance}} = \frac{23 \text{ minutes}}{2 \text{ miles}} = 11.5 \text{ minutes per mile} \]
Now, to find out how long it will take her to run 10 miles, we multiply her pace by the total number of miles:
\[ \text{Time for 10 miles} = \text{Pace} \times \text{Distance} = 11.5 \text{ minutes per mile} \times 10 \text{ miles} = 115 \text{ minutes} \]
So, it will take Mary 115 minutes to run 10 miles.