To find out how many questions per minute you were answering, we need to calculate the average speed of answering questions for each segment of the exam:
Let's assume that in the first 10 questions, you took x minutes to answer them.
So, the remaining 11 questions must be answered twice as fast, which means you have 48 minutes - x minutes to answer them.
To calculate the average speed of answering questions, we divide the number of questions by the number of minutes.
For the first 10 questions, the speed is: 10 questions / x minutes = 10/x questions per minute.
For the remaining 11 questions, the speed is: 11 questions / (48 - x) minutes = 11/(48 - x) questions per minute.
Since you need to answer the remaining questions twice as fast, we can set up the following equation:
10/x = 2 * 11/(48 - x).
To solve this equation, we can cross-multiply:
10(48 - x) = 2 * 11 * x.
Expanding and simplifying:
480 - 10x = 22x.
Rearranging:
480 = 22x + 10x,
480 = 32x,
x = 480/32,
x = 15.
Therefore, you were answering the first 10 questions at a rate of 10/15 = 2/3 questions per minute.