Question

Two carpenters are going to work together building a shed. The first carpenter estimates that it will take him 3 hours to build a shed, the other carpenter estimates it will take him 7 hours to build a shed. Working together, how long should it take them to build one shed?

Answer 1

If Both carpenters working together
`2(1)/(10)` hours or 2.1 hours will take to build one shed.

Explanation:

The given is,

First carpenter estimates that it will take him 3 hours to build a shed

Other carpenter estimates it will take him 7 hours to build a shed

Step:1

Formula to find 1 hour work of carpenters (Ref. Dr. R.S. Aggarwal book)

One hour's work =
`(1)/(n)`

Where, n - Number of working hours

From the given,

First carpenters one hour work =
`(1)/(3)`

Other carpenters one hour work =
`(1)/(7)`

If both are working together,

One hour work of both carpenters =
`((1)/(3) + (1)/(7) )`

=
`((7 + 3)/(21) )`

One hour work of both carpenters
`= (10)/(21)`

First carpenter and second carpenter will complete to build the shed in

=
`(21)/(10)` hours =
`2(1)/(10)` hours

Result:

If Both carpenters working together
`2(1)/(10)` hours or 2.1 hours will take to build one shed.