To determine how many minutes Rachael takes per kilometer for a water break, we first need to calculate how much time she would spend running the entire race without breaks. Since Rachael can run 1 kilometer in 7.5 minutes, for a 5-kilometer race, the total running time would be:
\[ \text{Total running time} = 5 , \text{kilometers} \times 7.5 , \text{minutes/kilometer} = 37.5 , \text{minutes} \]
Rachael's goal is to complete the race in 38.75 minutes, which means she has:
\[ \text{Extra time for breaks} = \text{Goal time} - \text{Total running time} = 38.75 , \text{minutes} - 37.5 , \text{minutes} = 1.25 , \text{minutes} \]
Now, Rachael takes a water break at the halfway point between each kilometer marker. In 5 kilometers, there are four break points:
- After 1 kilometer
- After 2 kilometers
- After 3 kilometers
- After 4 kilometers
Thus, there are four breaks in total.
To find out how much time she can spend on each water break, we divide the total extra time by the number of breaks:
\[ \text{Time per break} = \frac{\text{Extra time for breaks}}{\text{Number of breaks}} = \frac{1.25 , \text{minutes}}{4} = 0.3125 , \text{minutes} \]
So, Rachael can take approximately 0.3125 minutes per kilometer for a water break, which is equivalent to 18.75 seconds per break.