Michael has constructed a device that fits on the end of a water hose. With this device, he can adjust the diameter of a tube connected to the end of the hose. He has found that the speed of the water coming out of the hose varies inversely with the diameter of the tube at the end of the hose. With the diameter set at .6 inches, the water will come out of the hose at a speed of 5 feet per second. How fast will the water be moving out of the tube if its diameter is reduced to .2 inches?

Question

anonymous · Answer

All you need to do is take the fact that the speed of the water is inversely proportional to the diameter of the tube, so you can write something along the lines of:
$$v = \frac{ k }{ d }$$
Where v is the water's velocity, d is the tube's diameter, and k is a constant.
Then you can substitue the data you're given into the equation to find k, then use your equation to find v when d = 0.2.