Water is drained from a vertical cylindrical tank by opening a valve at the base of the tank. It is known that the rate at which the water level drops is proportional to the square root of water depth $y,$ where the constant of proportionality $k>0$ depends on the acceleration due to gravity and the geometry of the hole. If $t$ is measured in minutes and $k=\frac{1}{15},$ then the time to drain the tank if the water is 4 m deep to start with is (a) 30 min (b) 45 min (c) 60 min (d) 80 min

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