Two rectangular water tanks stand side by side on the ground, tank A measures 2.1m long, 2.6m wide and 2.0m high, tank B measures 2.7m long, 3m wide and 2m high. Tank A contains water up to a height of 1.43m, but tank B is filled all the way up. A pipe was opened that lets water flow from tank B to tank A at a rate of 9 litres per minute. How long will it take until the height of the water is the same in both tanks?
Question
Two rectangular water tanks stand side by side on the ground, tank A measures 2.1m long, 2.6m wide and 2.0m high, tank B measures 2.7m long, 3m wide and 2m high. Tank A contains water up to a height of 1.43m, but tank B is filled all the way up. A pipe was opened that lets water flow from tank B to tank A at a rate of 9 litres per minute. How long will it take until the height of the water is the same in both tanks?
Solution
To solve this problem, we first need to calculate the volume of water in each tank and the volume needed to equalize the water level in both tanks.
Step 1: Calculate the volume of water in each tank.
The volume of a rectangular tank (or any rectangular prism) is given by the formula: Volume = length x width x height.
For tank A, the volume of water is: 2.1m x 2.6m x 1.43m = 7.798 cubic meters.
For tank B, the volume of water is: 2.7m x 3m x 2m = 16.2 cubic meters.
Step 2: Calculate the volume needed to equalize the water level in both tanks.
The total volume of water in both tanks is: 7.798 cubic meters + 16.2 cubic meters = 23.998 cubic meters.
Since we want the water level to be the same in both tanks, we divide the total volume by 2: 23.998 cubic meters / 2 = 11.999 cubic meters.
Therefore, we need to transfer: 16.2 cubic meters - 11.999 cubic meters = 4.201 cubic meters from tank B to tank A.
Step 3: Calculate the time needed to transfer the water.
The pipe transfers water at a rate of 9 liters per minute. To convert this to cubic meters per minute, we use the fact that 1 cubic meter = 1000 liters. So, the pipe transfers water at a rate of 9 / 1000 = 0.009 cubic meters per minute.
Therefore, the time needed to transfer the water is: 4.201 cubic meters / 0.009 cubic meters per minute = 467 minutes.
So, it will take approximately 467 minutes (or about 7 hours and 47 minutes) to equalize the water level in both tanks.
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