# How long will it take Princess to finish the paper if she works by herself?Marie, Princess and Sarah have to complete a term paper on the life of the great Mathematician Blaise Pascal. If they...

How long will it take Princess to finish the paper if she works by herself?

Marie, Princess and Sarah have to complete a term paper on the life of the great Mathematician Blaise Pascal. If they work together they can finish the paper in 1 week. If only Sarah and Marie work, they need 10 days to complete the report.

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### 2 Answers

Marie, Princess and Sarah have to complete a term paper on the life of the great Mathematician Blaise Pascal. If they work together they can finish the paper in 1 week. If only Sarah and Marie work, they need 10 days to complete the report.

The time taken by Princess to complete the paper on her own has to be determined. Let it be P.

As all the three finish the paper in 7 days, they complete `1/7` of the paper per day. Sarah and Marie complete `1/10` of the paper per day. The rate at which Princess completes the paper is `1/P` . Also `1/P + 1/10 = 1/7`

`1/P = 1/7 - 1/10 = 3/70`

=> P = `70/3`

**Princess would take `70/3` days to complete the paper on her own.**

Let the work that Marie, Princess, and Sarah can do per day be a, b, c respectively.

In the conditions given by the question,

1/(a+b+c) = 10

1/(a+c)=7

=> a+b+c = 1/10

a+c = 1/7

Therefore, b, the work per day of princess, is

b = (a+b+c)-(a+c) = 1/7 - 1/10 = 3/70

The days that will be taken for princess to work alone is therefore, 70/3 days (about 24 days)