Two brigades had to build a house. The first brigade works alone and builds the house in 15days. The second brigade builds it in 30days. How long will it take to build the house when both brigades work together?
The combined effort is sum of the efforts.
Combined effort is
So, when both work together, they finish one unit in 10 days.
As each person is assumed to work at the same rate and the second brigade takes twice as long as the first; it implies that brigade 2 has 1/2 the membership as brigade 1
( 1/2 as many people means that they work twice as long)
So combining the two give
Consider brigade 1 as being unit the size man days.
Let the number of days be
Adding the two groups give
Choosing random numbers just for this demonstration:
3 people working 6 days gives
5 people working 10 days gives
So if 5 people did job 1