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. 48 minutes B. 55 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. 48 minutes B. 55 minutes C. 44 minutes D. 40 minutes
Solution
To solve this problem, we first need to find out 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 find out how much water the pipe can pump per hour.
The pipe pumps water at a speed of 6 km/h. However, the dimensions of the pipe are in meters, so we need to convert the speed to meters per hour.
1 km = 1000 m, so 6 km/h = 6000 m/h.
The pipe is also a rectangular prism, so its volume is also given by the formula: length x width x height.
The volume of water the pipe can pump per hour is: 1 m x 1 m x 6000 m = 6000 cubic meters.
Finally, we need to find out how long it takes for the pipe to pump 4000 cubic meters of water.
Time = Volume / Rate, so Time = 4000 cubic meters / 6000 cubic meters per hour = 0.67 hours.
To convert hours to minutes, we multiply by 60, so 0.67 hours x 60 minutes/hour = 40 minutes.
So, it will take 40 minutes for the water to rise by 2 m. The answer is D. 40 minutes.
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