Milly reads 20 pages in 4 minutes. Sara reads 12 pages in 3 minutes. Find each constant of proportionality and write a direct variation equation then.
To find the constant of proportionality, we divide the number of pages read by the corresponding number of minutes for each person.
For Milly, the constant of proportionality is 20/4 = 5 pages per minute.
For Sara, the constant of proportionality is 12/3 = 4 pages per minute.
The direct variation equation is y = kx, where y represents the number of pages read and x represents the number of minutes.
For Milly: y = 5x
For Sara: y = 4x
To find the constant of proportionality, we need to divide the number of pages read by the time it took to read them for each person.
For Milly:
Constant of proportionality = (number of pages read) / (time taken)
Constant of proportionality for Milly = 20 / 4 = 5 pages per minute
For Sara:
Constant of proportionality = (number of pages read) / (time taken)
Constant of proportionality for Sara = 12 / 3 = 4 pages per minute
Now, we can write a direct variation equation using the formula y = kx, where y is the dependent variable (number of pages read), x is the independent variable (time taken), and k is the constant of proportionality.
Direct variation equation for Milly: y = 5x
Direct variation equation for Sara: y = 4x
In these equations, the number of pages read is directly proportional to the time taken for both Milly and Sara.
To find the constant of proportionality for each scenario, we can divide the number of pages read by the time taken.
For Milly:
Constant of proportionality = 20 pages / 4 minutes
Constant of proportionality = 5 pages/minute
For Sara:
Constant of proportionality = 12 pages / 3 minutes
Constant of proportionality = 4 pages/minute
Now, let's write the direct variation equation for each person:
For Milly:
Let x represent the number of minutes.
Number of pages Milly can read (y) = constant of proportionality (5) * x
So, the direct variation equation for Milly is:
y = 5x
For Sara:
Let x represent the number of minutes.
Number of pages Sara can read (y) = constant of proportionality (4) * x
So, the direct variation equation for Sara is:
y = 4x