How long does it take pumps a and b working together to empty New Orleans, working together:
A) pump a takes 10 days and pump b takes 15 days..
B) pump a takes 21 weeks and pump b takes 28 weeks..
C) pump a takes 44 months and pump b takes 77 months

The way to solve a problem like this is to consider the rate each pump works and then add the rates when the pumps are working together. So for the first problem pump A clears 1 flood per 10 days - so its rate is 1/10 flood/day - and pump B's rate is 1/15 floods per day. Working together they clear (1/10 + 1/15) floods/day = (1/6) flood per day. So the amount of time it takes to clear one flood working together is (1 flood)/(1/6 floods/day) = 6 days.