Question 708075
If they work together, we are assuming their rates are additive.

Cara does 1 barrel in 30 minutes, rate is 1/30.
Jack's work rate is 1/42 barrels per minute.


Working together, their rate is {{{1/30+1/42}}}.


Using the relation rate*time=jobs, to do ONE job, (fill 1 barrel), we have
{{{(1/30+1/42)*t=1}}}.


The number of minutes then for both of them doing this one job is
{{{t=1/(1/30+1/42)}}}.



Just look at the rate and simplify that first:
{{{r=(7+5)/(2*3*5*7)}}}
{{{r=12/72}}}
{{{r=1/6}}},  1 barrels in 6 minutes


Refer back a bit to {{{t}}}, that job is done in 6 minutes.