Rachael is running a 5-kilometer race with 200 participants. She knows she can complete 1 kilometer in 7.5 minutes, and she plans to keep that pace for the whole race. However, she wants to give herself some extra time to take a water break at the halfway point between each kilometer marker. Her goal is to complete the race in 38.75 minutes, and she needs to figure out how much time she can take for each water break.

Question

\]She creates the following table to figure out her time at each kilometer.


Kilometers Run
1
2
3
4
5

Time(minute)

7.75

15.5

23.25

31

38.75



How many minutes does Rachael take per kilometer for a water break?
Enter your answer as a decimal without units, like this: 42.25

Answer 1

To determine how much time Rachael can take for water breaks per kilometer, we start by calculating her total running time for the 5-kilometer race at her pace of 7.5 minutes per kilometer.

The total time to run 5 kilometers is: \[ 5 \text{ kilometers} \times 7.5 \text{ minutes/kilometer} = 37.5 \text{ minutes} \]

Next, we look at her goal to complete the race in 38.75 minutes. We can find out how much time she has available for water breaks by subtracting her total running time from her goal time: \[ 38.75 \text{ minutes} - 37.5 \text{ minutes} = 1.25 \text{ minutes} \]

Now, she needs to determine how much time she can allocate for each water break. Since she takes a water break at the halfway point between each kilometer, she will have a water break after the following intervals:

• After kilometer 1
• After kilometer 2
• After kilometer 3
• After kilometer 4
• (No break after kilometer 5, since that’s the finish.)

This means she will take a total of 4 water breaks (after the first four kilometers). Therefore, we divide the total time she has available for breaks by the number of breaks: \[ \text{Time per water break} = \frac{1.25 \text{ minutes}}{4 \text{ breaks}} = 0.3125 \text{ minutes} \]

Thus, Rachael takes 0.3125 minutes per kilometer for a water break.