It takes Julian 1/2 hour to walk 2 miles. He decides to start walking in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. At which ratio does the constant of proportionality appear
To determine the ratio at which the constant of proportionality appears in the given data table, we need to first analyze the relationship between time and distance.
According to the information provided, Julian takes 1/2 hour to walk 2 miles. We can write this relationship as:
Time (in hours) = Distance (in miles) / Rate (in miles per hour)
Let's fill in the values in the data table with the given information:
| Time (hours) | Distance (miles) |
|--------------|-----------------|
| 1/2 | 2 |
We can see that when Julian walks for 1/2 hour, he covers a distance of 2 miles.
Now, let's calculate the rate (in miles per hour):
Rate (in miles per hour) = Distance (in miles) / Time (in hours)
= 2 miles / (1/2) hours
= 4 miles per hour
So, the constant of proportionality, which is the rate at which Julian walks, is 4 miles per hour. Thus, the ratio at which the constant of proportionality appears in the data table is 4:1.
Ruth can read 15 pages in 30 minutes. She decides to create a table to keep track of her progress. From the data provided, at what ratio is the constant of proportionality?
To determine the ratio at which the constant of proportionality appears in the given data, we need to analyze the relationship between the number of pages read and the time taken.
According to the information provided, Ruth can read 15 pages in 30 minutes. We can write this relationship as:
Number of pages read = Time taken (in minutes) × Rate (in pages per minute)
Let's fill in the values in the data table with the given information:
| Time taken (minutes) | Number of pages read |
|----------------------|---------------------|
| 30 | 15 |
We can observe that when Ruth reads for 30 minutes, she reads 15 pages.
Now, let's calculate the rate (in pages per minute):
Rate (in pages per minute) = Number of pages read / Time taken (in minutes)
= 15 pages / 30 minutes
= 0.5 pages per minute
So, the constant of proportionality, which is the rate at which Ruth reads, is 0.5 pages per minute. Thus, the ratio at which the constant of proportionality appears in the data table is 0.5:1 or 1:2.
simplify
The ratio 0.5:1 can be simplified by multiplying both parts of the ratio by 2:
0.5 × 2 : 1 × 2
This gives us the simplified ratio of 1:2. Therefore, the simplified ratio at which the constant of proportionality appears is 1:2.
Determine if the quantities in the data table re in a proportional relationship. If they do not have a proportional relationship, indicate why.
To determine if the quantities in the data table are in a proportional relationship, we need to see if the ratio between the two quantities remains constant. Let's analyze the data table provided:
| Time taken (minutes) | Number of pages read |
|----------------------|---------------------|
| 30 | 15 |
To check if the quantities are in a proportional relationship, we can calculate the ratio between the two quantities:
Ratio = Number of pages read / Time taken (in minutes)
For the given data:
Ratio = 15 pages / 30 minutes
Simplifying the ratio gives:
Ratio = 0.5 pages per minute
Since the ratio between the number of pages read and the time taken is 0.5 pages per minute and not a constant value, we can conclude that the quantities in the data table do not have a proportional relationship. The reason for this is that the rate at which Ruth reads is not constant; it varies with time.