You have 48 minutes to take an exam of 21 questions. After you finish the first 10 questions, you realize you must answer the remaining questions twice as fast to finish the exam.
How many questions per minute were you answering?
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.
To determine the number of questions per minute you were answering, we can follow these steps:
1. Calculate the total time you have to complete the exam. In this case, it is 48 minutes.
2. Determine the number of questions you can answer in the first 10 minutes. Since you have to finish the remaining questions twice as fast, you can answer (10 / 2) = 5 questions in the remaining time.
3. Calculate the total number of questions you can answer in 48 minutes. In the first 10 minutes, you answered 10 questions, and in the remaining time, you answered 5 questions. Therefore, you answered 10 + 5 = 15 questions in total.
4. Divide the total number of questions by the total time taken. In this case, you answered 15 questions in 48 minutes. Therefore, the number of questions per minute you were answering is (15 / 48) ≈ 0.3125 questions per minute.
So, you were answering approximately 0.3125 questions per minute.