time and work

Question

Mason A can build a shed in 12 hrs .Mason B takes 9 hrs while mason C takes 12 hrs to do the same job.If all three masons are put to work together how long will they take to build the shed ?How will the payment of spanish dollar 1000 for the job be distributed among the three.

Answer 1

(1/12) + (1/9) + (1/12) = 1/x

 

(3 + 4 + 3)/36 = 1/x

 

x = 36/10 = 3 3/5

 

It is always hard to explain why work problems almost always look as if they involve reciprocals; it is be cause the fractions are rates, e.g. the unit on 1/12 is house/hr.  Then the time each person work becomes a common multiplier which divides out and the equation written first emerges.