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Can somebody tell me how to solve this problem?

"Last Thursday, Brandon was awake for 2/3 of the total time in the day.
He spent 1/4 of his waking hours reading science fiction books.
What fraction of the total time in the day did Brandon spend reading science fiction books?"


Total time of day = 24 hrs
  2   x 24 = 16 hrs
So, Brandon was awake for 16 hrs.
He spent one-fourth of his waking hrs reading science fiction books.
So, he spent,   x 16 = 4 hrs
Out of 16 hrs, he spent 4 hrs reading science fiction books.
So, he spent  hrs. reading, i.e.,  divided by 41
                   16                           16                4    4
Brandon spent 1 hrs reading.
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Brandon was awake for 2/3day =24*2/3=16 hours
Time spent for reading fiction ⇒ 16*1/4= 4 hours
 Fraction of day reading fiction⇒4/24=1/6
Answer  1/6
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