I believe that we need to know something about at least one of the individual's rate of work per minute to have a definite solution for this.
Note that Mike and Joshua must do 1/120 of the job in one minute [since it takes them 120 minutes for the whole job]
And Mike and Kelvin must do 1/180 of the job in one minute [ since it takes them 180 minutes for the whole job ]
Let M be the part of the job that Mike can do in one minute , J the part of the job that Joshua can do in one minute and K the part of the job that Kelvin can do in one minute
Then we have the following system
M + J = 1/120
M + K = 1/180
Subtracting the second equation from the first, we have that J - K = 1/360....i.e., Joshua can do 1/360 more of the job per minute than Kelvin can
Suppose that Mike can do 1/200 of the job each minute
Then Joshua can do 1/300 of the job each minute and Kelvin can do 1/1800 of the job each minute......and 1/300 - 1/1800 = 1/360
Or......suppose that Mike can do 1/300 of the job each minute
Then Joshua can do 1/200 of the job each minute and Kelvin can do 1/450 of the job each minute
And 1/200 - 1.450 = 1/360
Thus....there are infinite solutions to this......all we definitely know is that each person must do less than 1/180 of the job every minute
