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 $2\frac{1}{10}$ hours or 2.1 hours will take to build one shed.

Step-by-step 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 = $\frac{1}{n}$

    Where, n - Number of working hours

     From the given,

     First carpenters one hour work = $\frac{1}{3}$

     Other carpenters one hour work = $\frac{1}{7}$

     If both are working together,

     One hour work of both carpenters = $(\frac{1}{3} + \frac{1}{7} )$

                                                                 = $(\frac{7 + 3}{21} )$

      One hour work of both carpenters  $= \frac{10}{21}$

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

                                                     = $\frac{21}{10}$ hours = $2\frac{1}{10}$ hours

Result:

             If Both carpenters working together $2\frac{1}{10}$ hours or 2.1 hours will take to build one shed.