What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?A certain lock for raising and lowering barges from one river level to another is a rectangular parallelepiped 200 meters long, 50 wide, and 20 deep. A barge is floating in the lock that is also a rectangular parallelepiped measuring 80 meters long, 25 wide, and 5 deep. The barge, containing 3,000 barrels of toxic chemicals, displaces 8,000 long tons of water. The water has a density of one long ton per cubic meter. Each barrel is watertight, with a volume of one cubic meter and a weight of two long tons. A group of terrorists render the lock inoperable and attach a time bomb to the side of the barge set to go off in three hours. The barge contains elevators for moving barrels quickly to the deck, but the crew is too shorthanded to roll the heavy barrels up an inclined plane in the time allotted. The deck is only ten centimeters below the top edge of the lock, from which the barrels could be rolled to dry land. If no water is entering or leaving the lock, how many barrels at a minimum would have to be rolled into the water in the lock in order to raise the level of the barge so that its deck would be even with or slightly above the top edge of the lock so that the remaining barrels can be rolled to dry land?
Then where did you go - what did you find?When I approached this problem initially, I focused in on a few pieces of critical information and ignored superfluous information in the question. The volume of the lock, especially the depth, the density of the water, and how much water each barrel displaces (calculated by looking at the bolded parts below) I viewed as critical information. I focused on the volume of the lock, especially the depth, because the question wants to know how many barrels have to be dumped overboard to raise the lock's level by 10 centimeters.
The water has a density of one long ton per cubic meter. Each barrel is watertight, with a volume of one cubic meter and a weight of two long tons.
200*50 = 10000 m^2
A certain lock for raising and lowering barges from one river level to another is a rectangular parallelepiped 200 meters long, 50 wide, and 20 deep. A barge is floating in the lock that is also a rectangular parallelepiped measuring 80 meters long, 25 wide, and 5 deep. The barge, containing 3,000 barrels of toxic chemicals, displaces 8,000 long tons of water. The water has a density of one long ton per cubic meter. Each barrel is watertight, with a volume of one cubic meter and a weight of two long tons. A group of terrorists render the lock inoperable and attach a time bomb to the side of the barge set to go off in three hours. The barge contains elevators for moving barrels quickly to the deck, but the crew is too shorthanded to roll the heavy barrels up an inclined plane in the time allotted. The deck is only ten centimeters below the top edge of the lock, from which the barrels could be rolled to dry land. If no water is entering or leaving the lock, how many barrels at a minimum would have to be rolled into the water in the lock in order to raise the level of the barge so that its deck would be even with or slightly above the top edge of the lock so that the remaining barrels can be rolled to dry land?