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

Alexis1415 · Answer

A diameter of 0.2 inches would make the speed of the water come out at 15 feet per second.

If the diameter is = 0.6 inches  and the speed of the water coming out is 5 feet per second.

If the diameter is = 0.2 inches, then we need to find how much water is coming out.

So what we have collected is the diameters: 0.6 inches and 0.2 inches, Then we found out the speed of sed 0.6 inches which is 5 feet and 0.2 is x (not determined yet).

Since this makes them inversely related it becomes,
$$\frac{ 0.6 }{ 0.2 } = \frac{ x }{ 5 }$$

Then, 
$$0.6  \times 5=0.2x$$
$$3=0.2x$$
$$x=\frac{ 3 }{ 0.2 }$$
$$x=15$$

D3AD4YOU · Answer

Here's what i came up with!

D3AD4YOU · Answer

ter of the tube. Thus, if he decreases the diameter of the tube by a factor of 2, then the speed of the water coming out of the tube will be doubled. If he increases the diameter of the tube by a factor of 3, then the speed of the water will be decreased by a factor of 3.

So, if Michael decreases the diameter of the tube by a factor of x, then the speed of the water coming out of the tube will be increased by a factor of 1/x. Similarly, if he increases the diameter of the tube by a factor of x, then the speed of the water will be decreased by a factor of x.