precalculus word problem

Question

An aquarium tank can hold 7700

liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 44

minutes. The second pipe can fill the tank in 77

minutes by itself. When both pipes are working together, how long does it take them to fill the tank ?

Answer 1

The rate for first pipe =7700/44=175 L/min

The rate for Second pipe =7700/77=100 L/min

The time to fill the tank by two pipes T:

175*T+100T=7700 L

T=7700/275=28 min

Answer 2

So, the tank holds 7700L. We need to find the rate (liters per minute) at which the two pipes fill the tank.

The first pipe fills the 7700L tank in 44 minutes, so the rate is 7700/44 liters per minute.

The second pipe fills the 7700L tank in 77 minutes, so the rate is 7700/77 liters per minute.

We have 7700 = 77*100 = 7*11*25*4 = (4*11)*(7*25) = 44*175, and so 7700L/44min = 175 L/min.

Next, we have 7700 = 77*100, so 7700L/77min = 100 L/min.

Since the pipes don't affect one another, the pipes fill the tub at these rates simultaneously. The tank will be filled at the rate of 175L/min + 100L/min = 275L/min.

Finally, 7700L / (275L/min) = 7700L*min / 275L = 7700min / 275 = (7700/275) min = (77*100/(11*25)) min = (7*11*4*25/(11*25)) min = 7*4 min = 28 minutes. We divide because we need the units to match up.