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A receptionist can type documents 4 times as fast as her assistant. Working together, they can type up a day's worth of documents in 3

hours. On a day that the assistant is absent from work, find the number of hours, n. that it will take the receptionist to type up the day's
documents on her own.

User Jay Wilde
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1 Answer

24 votes
24 votes

Answer:

3.75 hours

Explanation:

The receptionist takes n hours to do 1 day's worth of work.

The assistant takes 4n hours to the 1 day's worth of work.

In 1 hour, the receptionist does 1/n amount of work.

In 1 hour, the assistant does 1/(4n) amount of work.

Working together, in 1 hour, they do this amount of work:

1/n + 1/(4n)

Working together, the 2 workers do the job in 3 hours.

Working together, in 1 hour, they do this amount of work:

1/3

1/n + 1/(4n) = 1/3

Multiply both sides of the equation by the LCD, 12n.

12 + 3 = 4n

4n = 15

n = 15/4

n = 3.75

Answer: 3.75 hours

User OmniOwl
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