After 30 minutes, Sara has completed 22 math problems. If she has 67 total math problems completed after 45 minutes, at what rate is she completing the problems?
To find the rate at which Sara is completing the math problems, we need to calculate the number of problems she completes per minute.
First, we can calculate the number of math problems she completes in 1 minute by using a proportion:
22 problems / 30 minutes = x problems / 1 minute
Solving for x, we get:
x = (22 problems / 30 minutes) * 1 minute = 0.73 problems per minute
This means that Sara is completing 0.73 math problems per minute in the first 30 minutes.
Next, we can calculate the number of math problems she completes in the next 15 minutes (from 30 to 45 minutes):
67 total problems - 22 problems completed in the first 30 minutes = 45 problems completed in the next 15 minutes
To find the rate at which she completed these problems, we can use the same proportion:
45 problems / 15 minutes = x problems / 1 minute
Solving for x, we get:
x = (45 problems / 15 minutes) * 1 minute = 3 problems per minute
This means that Sara is completing 3 math problems per minute in the next 15 minutes.
Therefore, her overall rate of completing math problems is:
(22 problems / 30 minutes * 1 minute) + (45 problems / 15 minutes * 1 minute) = 0.73 + 3 = 3.73 problems per minute
So, Sara is completing the math problems at a rate of 3.73 problems per minute.