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 ( 1,30). (1 1-2,30) (15,1/2) (2,60)
To find the constant of proportionality, we can use the ratio of any two pairs of values given. Let's calculate the ratios for each pair:
1st Pair: (1, 30)
The ratio is given by 30/1 = 30.
2nd Pair: (1 1/2, 30)
The ratio is given by 30/(3/2) = 20.
3rd Pair: (15, 1/2)
The ratio is given by (1/2)/15 = 1/30.
4th Pair: (2, 60)
The ratio is given by 60/2 = 30.
Therefore, the constant of proportionality is 30.
To find the constant of proportionality, we need to determine the ratio between the number of pages read and the corresponding time taken.
Using the provided data points:
(1, 30) implies 1 page read in 30 minutes.
(1 1/2, 30) implies 1.5 pages read in 30 minutes.
(15, 1/2) implies 15 pages read in 0.5 (1/2) minutes.
(2, 60) implies 2 pages read in 60 minutes.
To calculate the ratios:
For the first data point (1, 30), the ratio is 1/30 = 1 / (1 * 30) = 1/ (1*1+0) = 1/1 = 1.
For the second data point (1 1/2, 30), the ratio is (1 1/2) / 30 = (3/2) / (1*30) = (3/2) / (1/1 +0) = (3/2) / (1/1) = 3/2.
For the third data point (15, 1/2), the ratio is 15 / (1/2) = 15 / (1/1+(-1)) = 15 / (1/1) = 15/1 = 15.
For the fourth data point (2, 60), the ratio is 2 / 60 = 2 / (1*60) = 2 / (1/1 +0) = 2 / (1/1) = 2.
Therefore, the ratios at which the constant of proportionality can be observed are:
1, 3/2, 15, 2.
To determine the constant of proportionality, we can use the formula:
Constant of proportionality = y/x
where y is the dependent variable and x is the independent variable.
In this case, the number of pages Ruth can read is the dependent variable (y), and the time it takes her to read those pages is the independent variable (x).
Let's calculate the ratio for each set of data:
First data point: (1, 30)
Constant of proportionality = 30/1 = 30
Second data point: (1 1-2, 30)
To convert the mixed fraction 1 1-2 into an improper fraction, we add the whole number (1) to the product of the denominator (2) and the numerator (1) and place the sum over the denominator.
1 1-2 = (2+1)/2 = 3/2
Constant of proportionality = 30 / (3/2) = 30 * (2/3) = 20
Third data point: (15, 1/2)
Constant of proportionality = (1/2) / 15 = 1 / (2*15) = 1/30
Fourth data point: (2, 60)
Constant of proportionality = 60 / 2 = 30
So, the ratios for the given data sets are:
(1, 30): 30
(1 1-2, 30): 20
(15, 1/2): 1/30
(2, 60): 30
Therefore, the constant of proportionality for each ratio is 30, 20, 1/30, and 30, respectively.