SOLUTION: 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

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 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       Log On


   

Question 1202875: 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
Found 3 solutions by papachick24025, josgarithmetic, greenestamps:
Answer by papachick24025(6) About Me  (Show Source):
You can put this solution on YOUR website!
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.

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
---------
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%2F3 of "time" remained for use after the English homework.
Half of that is 1%2F6.
1%2F6 of "time" was for Science homework. The other 1%2F6 of time was for Math homework.
%281%2F6%29t=20--------unit of MINUTES

Total study time 6%2A20=highlight_green%28120%29

The question, how much time on English?
%282%2F3%29120=highlight%2880%29

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Note the wording in the statement of the problem does not correctly convey the intended information:

"...spent the rest of the 20 minutes on..."

That is surely supposed to say

"...spent the remaining 20 minutes on..."

Getting past the sloppy wording......

After the English homework, he spent half of the remaining time on Science homework. That means the remaining 20 minutes that he spent on Math homework were the other half of the time remaining after the English homework.

So he spent a total of 40 minutes on the Science and Math homework.

He spent 2/3 of his total time on his English homework, so the 40 minutes he spent on Science and Math was 1/3 of the total time.

So he spent a total of 3(40) = 120 minutes on his homework, which means he spent 120-40 = 80 minutes on English homework.

ANSWER: 80 minutes