To find out how much time Rachael takes for each water break, we first need to calculate the total time it takes her to run the race without any breaks and compare it to her goal time.
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Rachael can complete 1 kilometer in 7.5 minutes.
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Therefore, for 5 kilometers, her running time alone would be: \[ 5 \text{ km} \times 7.5 \text{ minutes/km} = 37.5 \text{ minutes} \]
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Rachael's goal is to finish the race in 38.75 minutes.
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Now, we find the difference between her goal time and her running time: \[ \text{Extra time for breaks} = \text{Goal time} - \text{Running time} \] \[ \text{Extra time for breaks} = 38.75 \text{ minutes} - 37.5 \text{ minutes} = 1.25 \text{ minutes} \]
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She runs a total of 5 kilometers and will take a water break at the halfway point between each kilometer marker. This means she will take breaks after the following kilometers:
- After 1 km
- After 2 km
- After 3 km
- After 4 km
This results in 4 breaks.
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To find out how much time she can take for each water break, divide the total extra time by the number of breaks: \[ \text{Time per break} = \frac{\text{Extra time for breaks}}{\text{Number of breaks}} \] \[ \text{Time per break} = \frac{1.25 \text{ minutes}}{4} = 0.3125 \text{ minutes} \]
So, Rachael takes 0.3125 minutes per kilometer for a water break.
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