Question

In 40 minutes, John can run 20 laps around the track. Determine the number of laps he can run per hour. Find the constant of proportionality in this situation.
30 laps/hour and 1/2
60 laps/hour and 1/4
15 laps/hour and 1/3
20 laps/hour and 1/2

Answer 1

To find the number of laps John can run per hour, we first determine how many laps he runs in one minute.

John runs 20 laps in 40 minutes. To find the number of laps he runs in one minute, we calculate:

\[
\text{Laps per minute} = \frac{20 \text{ laps}}{40 \text{ minutes}} = \frac{1}{2} \text{ laps per minute}
\]

Now, to find how many laps he can run in one hour (which is 60 minutes), we multiply the laps per minute by the number of minutes in an hour:

\[
\text{Laps per hour} = \left(\frac{1}{2} \text{ laps per minute}\right) \times 60 \text{ minutes} = 30 \text{ laps}
\]

Now, we recognize that the constant of proportionality in this situation relates the number of laps to the time it takes. Since John runs \(\frac{1}{2}\) laps per minute, this is the constant of proportionality.

Thus, the final results are:
- Number of laps he can run per hour: **30 laps/hour**
- Constant of proportionality: **1/2**

So, the correct answer from the options given is:
**30 laps/hour and 1/2**.