- Determine the time for one lap by dividing the total time by the number of laps: \(\frac{24}{15} = 1.6\) minutes per lap.
- Calculate the time for 5 laps: \(5 \times 1.6 = 8\) minutes.
- Calculate the time for 20 laps: \(20 \times 1.6 = 32\) minutes.
- The time taken for 5 laps is \(\boxed{8 \text{ minutes}}\) and the time for 20 laps is \(\boxed{32 \text{ minutes}}\).
Explanation
- Analyzing the Proportional Relationship
Mei completes 15 laps in 24 minutes. Assuming her speed is constant, the time required to complete any number of laps is proportional to the number of laps completed. We are given the data:
- 15 laps take 24 minutes.
- We need to find the time for 5 laps and 20 laps.
Since the speed is constant, we can use the ratio of minutes to laps.
The time for 15 laps is 24 minutes, so the time for 1 lap is \(\frac{24}{15}\) minutes.
Simplifying this fraction by dividing both numerator and denominator by 3 gives:
\(\frac{24 \div 3}{15 \div 3} = \frac{8}{5} = 1.6\) minutes per lap.
- Calculating the Time for 5 Laps
To find the time for 5 laps, we can use the time per lap calculated in the previous step:
Time for 5 laps = 5 laps \(\times\) 1.6 minutes/lap = 8 minutes.
Alternatively, since 15 laps = 24 minutes, we can divide both quantities by 3 to get the time for 5 laps:
\(\frac{15}{3} = 5\) laps
\(\frac{24}{3} = 8\) minutes.
Thus, it takes Mei 8 minutes to complete 5 laps.
- Calculating the Time for 20 Laps
Now that we know it takes 8 minutes for 5 laps, we can easily calculate the time for 20 laps.
Since 20 laps is 4 times 5 laps (\(20 = 4 \times 5\)), the time taken for 20 laps will be 4 times the time taken for 5 laps:
Time for 20 laps = \(4 \times 8\) minutes = 32 minutes.
Alternatively, using the time per lap calculated earlier:
Time for 20 laps = 20 laps \(\times\) 1.6 minutes/lap = 32 minutes.
So, it takes Mei 32 minutes to finish 20 laps.
Examples
Proportionality is a fundamental concept used in everyday life, from cooking to travel. For example, if you are following a recipe that serves 4 people but you need to prepare food for 20 people, you use proportional scaling to adjust the quantities of your ingredients. Similarly, when planning a road trip, if you know your car consumes a certain amount of fuel for every 100 kilometers traveled, you can use ratios to estimate the total fuel required for your entire journey, ensuring you don't run out of gas mid-trip.