time (hours): 1/2 1 1 1/2 2
Pages read: 15 30 45 60
ruth can read 15 pages in 30 minutes she decides to create s table to keep track of her progress from the data provided at what radio is the constant proportionality
To find the constant proportionality, we can create a table of the time (hours) and the corresponding number of pages read:
Time (hours): 1/2 1 1 1/2 2
Pages read: 15 30 45 60
The constant proportionality can be found by dividing the number of pages read by the time taken for each interval:
For the first interval, from 1/2 hour to 1 hour, the number of pages read increases by 30 (from 15 to 30), while the time increases by 1/2 hour.
So, the constant proportionality for this interval is 30/0.5 = 60 pages per hour.
For the second interval, from 1 hour to 1 1/2 hours, the number of pages read increases by 15 (from 30 to 45), while the time increases by 1/2 hour.
So, the constant proportionality for this interval is 15/0.5 = 30 pages per hour.
For the third interval, from 1 1/2 hours to 2 hours, the number of pages read increases by 15 (from 45 to 60), while the time increases by 1/2 hour.
So, the constant proportionality for this interval is 15/0.5 = 30 pages per hour.
From the data provided, we can see that the constant proportionality is 30 pages per hour.
To find the constant proportionality, or the rate at which Ruth reads pages, we need to calculate the number of pages read per hour (proportionally).
We are given the data as follows:
Time (hours): 1/2, 1, 1 1/2, 2
Pages read: 15, 30, 45, 60
First, let's convert the time from hours to minutes because we know Ruth can read 15 pages in 30 minutes.
1/2 hour = 30 minutes
1 hour = 60 minutes
1 1/2 hours = 90 minutes
2 hours = 120 minutes
Now, we have the following data:
Time (minutes): 30, 60, 90, 120
Pages read: 15, 30, 45, 60
To find the rate, we will divide the number of pages read by the time in minutes.
Rate = Pages read / Time in minutes
For the first data point (30 minutes and 15 pages):
Rate = 15 / 30 = 0.5 pages per minute
For the second data point (60 minutes and 30 pages):
Rate = 30 / 60 = 0.5 pages per minute
For the third data point (90 minutes and 45 pages):
Rate = 45 / 90 = 0.5 pages per minute
For the fourth data point (120 minutes and 60 pages):
Rate = 60 / 120 = 0.5 pages per minute
From the calculations, we can see that the rate at which Ruth reads pages remains constant at 0.5 pages per minute or 30 pages per hour.
To find the constant proportionality, we need to determine the ratio of pages read to the corresponding time taken. Let's calculate the ratio for each data point:
For the first data point (time: 1/2 hour, pages read: 15):
Ratio = (pages read) / (time taken) = 15 / (1/2) = 30
For the second data point (time: 1 hour, pages read: 30):
Ratio = (pages read) / (time taken) = 30 / 1 = 30
For the third data point (time: 1 1/2 hours, pages read: 45):
Ratio = (pages read) / (time taken) = 45 / (3/2) = 30
For the fourth data point (time: 2 hours, pages read: 60):
Ratio = (pages read) / (time taken) = 60 / 2 = 30
As we can see, the ratio of pages read to time taken is consistently 30 for all the given data points. Therefore, the constant proportionality is 30.