Decide whether the rates are equivalent
A. 30 beats per 20 sec, 90 neats per 60 sec
B. 15 pages in 20 min., 10 pages in. 15 min
30/20 = 1.5 , 90/60 = 1/5 the same
15/20 = 3/4 , 10/15 = 2/3 NOT the same
To determine whether the rates are equivalent in each scenario, we need to compare the rates of change in both situations.
A. In the first scenario, we have 30 beats per 20 seconds and 90 beats per 60 seconds. We can simplify these rates to find a common denominator.
For the rate of 30 beats per 20 seconds, we can express it in terms of beats per second by dividing both the numerator and denominator by 20.
30 beats / 20 seconds = 1.5 beats / 1 second
For the rate of 90 beats per 60 seconds, we can express it as beats per second by dividing both the numerator and denominator by 60.
90 beats / 60 seconds = 1.5 beats / 1 second
Since both rates are equal to 1.5 beats per second, we can conclude that the rates of beats in scenario A are equivalent.
B. In the second scenario, we have 15 pages in 20 minutes and 10 pages in 15 minutes.
To compare these rates, we need to express them in terms of pages per minute.
For the rate of 15 pages in 20 minutes, we can calculate the rate of pages per minute by dividing both the numerator and denominator by 20.
15 pages / 20 minutes = 0.75 pages / 1 minute
For the rate of 10 pages in 15 minutes, we can convert it to pages per minute by dividing both the numerator and denominator by 15.
10 pages / 15 minutes = 0.67 pages / 1 minute
Since the rates are not equal (0.75 pages per minute and 0.67 pages per minute), we can conclude that the rates of pages in scenario B are not equivalent.