Question 171279
One of the hoses can fill the tank in 7 hours, so that hose can fill {{{1/7}}} of the tank in one hour.  Likewise, the other hose can fill {{{1/12}}} of the tank in one hour.


Using both hoses, you can fill {{{1/7+1/12=12/84+7/84=19/84}}} of the tank in one hour.


Therefore, both hoses can fill the tank in 84/19 hours, or just under 4 and a half hours (you can go ahead and calculate the hours, minutes, and seconds if you are so inclined).


In general, for two entities performing work, if entity 1 can do the entire job in {{{x[1]}}} hours and entity 2 can do the entire job in {{{x[2]}}} hours, then both working together can do the job in {{{(x[1]x[2])/(x[1]+x[2])}}} hours.


This is extensible to as many entities as you like simply by adding factors to the numerator and terms to the denominator.  For example, with three entities, the formula is:


{{{(x[1]x[2]x[3])/(x[1]+x[2]+x[3])}}}