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leonid [27]
2 years ago
7

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

s 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.
Mathematics
1 answer:
lora16 [44]2 years ago
7 0

Answer:

3.75 hours

Step-by-step 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

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