a small water pump would take 2 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time.

Let x be the time to fill together, thenx/2 + x/(1/2) = 1x + 4x = 25x = 2x = 2/5 hours = (2/5) hours x 60 min/hour = 24 minutes

The first one pumps at 1 tank per 2 hours, the second at 1 tank per 1/2 hour. So after t hours, the first pump will have filled (1/2)t of a tank, and second (1/0.5)t or simply 2t of a tank. We want these to add up to one full tank, so(1/2)t + (2)t = 1Solve this for t