John used a few hours to complete his homework. 2/3 of the time was spent on English homework. 1/2 of the remaining time was spent on Science
homework. He spent the rest of the 20 minutes on Math homework. How much time did he use to complete his English homework?
(1) 10 minutes
(2) 40 minutes
(3) 70 minutes
(4) 80 minutes
Let's start by finding out how much time John spent on Science and Math homework combined. We know that 2/3 of the total time was spent on English homework, so the remaining 1/3 of the time was spent on Science and Math combined.
1/3 of the time = 20 minutes (the time John spent on Math homework)
To find out how much time John spent on Science homework, we need to calculate 1/2 of the remaining time:
1/2 of 1/3 of the time = 1/6 of the total time
1/6 of the total time = 20 minutes (the time John spent on Math homework)
So John spent a total of 20 + 20 = 40 minutes on Science and Math combined.
Now we can calculate how much time John spent on English homework:
2/3 of the time = 2/3 * (total time)
2/3 * (total time) - 40 minutes = time spent on English homework
We don't know the total time, but we can use algebra to solve for it:
2/3 * (total time) - 40 minutes = time spent on English homework
2/3 * (total time) = time spent on English homework + 40 minutes
(total time) = (3/2) * (time spent on English homework + 40 minutes)
Now we can substitute the answer choices to see which one makes sense:
(1) If John spent 10 minutes on English homework, then the total time would be:
(total time) = (3/2) * (10 minutes + 40 minutes) = 75 minutes
This is not equivalent to the time John was given, which was a few hours.
(2) If John spent 40 minutes on English homework, then the total time would be:
(total time) = (3/2) * (40 minutes + 40 minutes) = 120 minutes
This is equivalent to the time John was given, so the answer is (2) 40 minutes.
To solve the problem, we need to use the given information to determine the amount of time John spent on English homework.
Let's start by using fractions to represent the time John spent on each subject:
- English homework: 2/3 of total time
- Remaining time: 1/3 of total time
- Science homework: 1/2 of remaining time = 1/2 * 1/3 = 1/6 of total time
- Math homework: rest of the time = total time - (English + Science) = 1 - (2/3 + 1/6) = 1/6 of total time
We know that John spent the rest of the 20 minutes on Math homework, so we can set up an equation:
1/6 * total time = 20 minutes
Solving for total time:
total time = 20 minutes / (1/6) = 120 minutes
Now we can find out how much time John spent on English homework:
English homework = 2/3 * total time = (2/3) * 120 minutes = 80 minutes
Therefore, the answer is (4) 80 minutes.
Note: It is important to understand that the time taken to complete homework may vary and may not be the same for everyone. This solution is based on the given information and assumptions made about the time fractions.
Let's solve this step by step:
Step 1: Calculate the total time John used for his homework.
Since he spent 20 minutes on Math, and Math was the last subject he worked on, we can assume that he spent the entire remaining time on his homework. Therefore, the total time he used for his homework is 20 minutes.
Step 2: Calculate the time John spent on Science homework.
We know that 1/2 of the remaining time was spent on Science. So, let's subtract the time spent on Math (20 minutes) from the total time (20 minutes):
Remaining time = Total time - Time spent on Math homework
Remaining time = 20 minutes - 20 minutes = 0 minutes
Since the remaining time is 0, it means that John did not spend any time on Science homework.
Step 3: Calculate the time John spent on English homework.
We know that 2/3 of the total time was spent on English. So, let's calculate 2/3 of the total time (20 minutes):
Time spent on English homework = (2/3) * Total time
Time spent on English homework = (2/3) * 20 minutes
Time spent on English homework = 40/3 minutes ā 13.33 minutes
Since it is not possible to spend 13.33 minutes on homework, we can round it to the nearest whole number. Therefore, John used approximately 13 minutes to complete his English homework.
So, the answer is:
John used approximately 13 minutes to complete his English homework.
Therefore, the correct option is (1) 10 minutes.