An experienced carpenter can frame a house twice as fast as an apprentice. Working together, it takes the carpenters 2 days. How long would it take the apprentice working alone?

We are required to calculate the number of days it would take the apprentice working alone

The number of days it takes the apprentice working alone is 6 days

let

Number of days taken for the carpenter to work alone = x

Number of days taken by the apprentice to work alone = 2x

Number of days taken to work together = 2 days

Work done per day Carpenter = 1/x

work done per day apprentice = 1/2x

work done per day together = 1/2

So,

work done per day together = Work done per day Carpenter + work done per day apprentice

1/2 = 1/x + 1/2x

1/2 = (2 + 1) / 2x

1/2 = 3/2x

cross product

1(2x) = 2(3)

2x = 6

x = 6/2

x = 3 days

Therefore,

Number of days taken by the apprentice to work alone = 2x

= 2(3)

= 6 days

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6 days

Step-by-step explanation:

Let the time taken by Carpenter working alone = days

Then time taken by apprentice alone = Twice as that of taken by Carpenter = 2 days

Time taken working together = 2 days

Work done in one day working together =

Work done in one day by Carpenter working alone =

Work done in one day by apprentice working alone =

Work done in one day by Carpenter working alone + Work done in one day by Carpenter working alone =  + = Work done in one day working together =

Time taken by Carpenter alone to complete the work = 3 days

Time taken by Apprentice alone to complete the work = 3 2= 6 days

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