The dimensions of a rectangular water tank are 10 m x 200 m x 6 m. If it is filled with a rectangular pipe of dimension 1 m x 1 m at a speed of 6 km/h, then in how much time will the water rise by 2 m? Ops: A. 55 minutes B. 48 minutes C. 44 minutes D. 40 minutes
Question
The dimensions of a rectangular water tank are 10 m x 200 m x 6 m. If it is filled with a rectangular pipe of dimension 1 m x 1 m at a speed of 6 km/h, then in how much time will the water rise by 2 m? Ops: A. 55 minutes B. 48 minutes C. 44 minutes D. 40 minutes
Solution
First, we need to calculate the volume of water needed to raise the water level by 2 m in the tank. The volume of a rectangular prism (or in this case, the water tank) is given by the formula length x width x height.
So, the volume of water needed is 10 m x 200 m x 2 m = 4000 cubic meters.
Next, we need to convert the speed of the water flow from km/h to cubic meters per second.
1 km/h = 1000 m/3600 s = 0.27778 m/s.
So, the speed of the water flow is 6 km/h x 0.27778 m/s = 1.6667 m/s.
However, the pipe is also 1 m x 1 m, so the actual volume of water flowing per second is 1.6667 cubic meters.
Finally, we divide the total volume of water needed by the volume of water flowing per second to find the time needed.
4000 cubic meters / 1.6667 cubic meters per second = 2400 seconds.
To convert seconds to minutes, we divide by 60.
2400 seconds / 60 = 40 minutes.
So, the water will rise by 2 m in 40 minutes. The answer is D. 40 minutes.
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