Question 828568
To start, form all the stated rates as "piece of work per day".


A&B:  1/6
B&C:  1/10
C&A:  1/15


The rates of any combination of these workers is the sum of the rate of the workers in the combination of workers.  


Looking at the combinations given, find that C&A rate is missing the rate of B.  Looking at A&B, and B&C, If you put these rates together, you find B occurs two times.  A&B+B&C-2B=C&A.  Putting that into the numeric information which corresponds, {{{1/6+1/10-2B=1/15}}}, permitting to find the rate for B if working alone.


Handle similarly with the other two individual rates.
B&C+C&A-2C=A&B
{{{1/10+1/15-2C=1/6}}}-----Solve for C.
'
C&A+A&B-2A=B&C
{{{1/15+1/6-2A=1/10}}}----Solve for A.


Each of the three equations gives the rate for the single unknown rate depending on whose rate is the unknown variable.