Question
Last year at a track meet, runner A and runner B both ran each of 4 laps in a race in 1.5 minutes. Runner A sets a goal for this year of changing his total time for the race by -0.12 minutes, with equal times for all 4 laps. Runner B sets a goal for this year of changing his time on each lap by -0.025 minutes.(1 point)
Use the drop-down menus to complete the statements.
Runner A's goal is to change his TIME on EACH LAP of the race by
minutes.
Runner B's goal is to change his TOTAL TIME for the RACE by
minutes.
Use the drop-down menus to complete the statements.
Runner A's goal is to change his TIME on EACH LAP of the race by
minutes.
Runner B's goal is to change his TOTAL TIME for the RACE by
minutes.
Answers
GPT-4o mini
To solve the problem, let's first calculate the total time for each runner last year.
Both runner A and runner B ran 4 laps, each taking 1.5 minutes per lap. Therefore, their total time for the race last year is:
- Total time for each runner = 4 laps × 1.5 minutes/lap = 6 minutes.
Now let's analyze the goals:
1. **Runner A's goal**: He aims to change his total time by -0.12 minutes. Since he runs 4 laps, he will need to divide this total change over the 4 laps. Therefore, the change in time per lap for Runner A is:
\[
\text{Change per lap} = \frac{-0.12 \text{ minutes}}{4} = -0.03 \text{ minutes.}
\]
2. **Runner B's goal**: He wants to change his time on each lap by -0.025 minutes. Since there are 4 laps, the total change in time for Runner B is:
\[
\text{Total change} = -0.025 \text{ minutes/lap} \times 4 \text{ laps} = -0.1 \text{ minutes.}
\]
Now, let's complete the statements:
1. Runner A's goal is to change his TIME on EACH LAP of the race by **-0.03** minutes.
2. Runner B's goal is to change his TOTAL TIME for the RACE by **-0.1** minutes.
Both runner A and runner B ran 4 laps, each taking 1.5 minutes per lap. Therefore, their total time for the race last year is:
- Total time for each runner = 4 laps × 1.5 minutes/lap = 6 minutes.
Now let's analyze the goals:
1. **Runner A's goal**: He aims to change his total time by -0.12 minutes. Since he runs 4 laps, he will need to divide this total change over the 4 laps. Therefore, the change in time per lap for Runner A is:
\[
\text{Change per lap} = \frac{-0.12 \text{ minutes}}{4} = -0.03 \text{ minutes.}
\]
2. **Runner B's goal**: He wants to change his time on each lap by -0.025 minutes. Since there are 4 laps, the total change in time for Runner B is:
\[
\text{Total change} = -0.025 \text{ minutes/lap} \times 4 \text{ laps} = -0.1 \text{ minutes.}
\]
Now, let's complete the statements:
1. Runner A's goal is to change his TIME on EACH LAP of the race by **-0.03** minutes.
2. Runner B's goal is to change his TOTAL TIME for the RACE by **-0.1** minutes.