Question

Laps

Time (minutes)
5
4
Noah ran laps around the school building.
number of laps is proportional to his time.
10
6
15
8
The table shows his times. He thinks the
Explain if Noah is right or wrong and why?

Answer 1

Explanation:

Answer 2

Noah is wrong. The number of laps is not proportional to his time.

While there seems to be a general trend of increasing time with increasing laps, the ratios between laps and time are not constant, which is a requirement for proportionality.

Here's why:

* **Ratio of laps to time for the first two data points:** 5 laps / 4 minutes = 1.25 laps/minute

* **Ratio of laps to time for the last two data points:** 10 laps / 6 minutes = 1.67 laps/minute

The ratios are not the same, indicating that the relationship is not proportional. As Noah runs more laps, he takes slightly longer per lap, even though the overall time increases.

Here's a table showing the ratios for each data point:

| Laps | Time (min) | Laps/Minute Ratio |

|---|---|---|

| 5 | 4 | 1.25 |

| 10 | 6 | 1.67 |

| 15 | 8 | 1.88 |

As you can see, the ratios increase as the number of laps increases. This means the relationship is not proportional, but rather shows a slight positive **non-linear** trend.

Therefore, Noah's assumption that the number of laps is proportional to his time is not accurate based on the given data.