A bathtub faucet has a maximum flow rate of 3 gal/min. The tub is rectangular (3 ft long x 2 ft wide x 1.5 ft deep). Although th
e tub drain is plugged, water leaks out at 0.01 gal/min. There is an overflow opening which allows water to drain from the tub. The overflow opening is 1 ft above the bottom of the tub. How long will it take the tub to fill to 1 ft deep with the faucet on at its maximum flow rate? If the area of the overflow opening is 0.5 in2 and water drains with a velocity of 1.8 ft/sec, will the tub ever overflow if you turn the faucet on at the maximum flow rate? If so, how long will it take? (Note: since the overflow opening is very small, assume that water drains through the entire opening once the water is 1 ft deep).
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