Volume help: flow rate 5gal/30s, find time to fill pool

[Emmigee]

Here is the problem.

At 9:00am on Saturday morning, I began to fill my totally empty swimming pool. To find the rate of flow of water, I filled a 5 gallon bucket in 30 seconds. At what time so I need to turn the hose off in order for the water to be 6 inches from overflowing?

Here is the picture to go with it.

Please do not just give an answer.
Steps to how you did it will be helpful as well.
I have to show all of my work. I just cannot figure out
what the shape in the middle is and how you would find
the volume of the whole thing.

I know that you need to find the volume in ft cubed and then convert it to gallons
and then you have to figure out how long for the amount of gallons, I just cannot figure
out the volume because of that middle shape.

Thank you.

 

[galactus]

Re: Volume help.

The middle shape is a trapezoid. Its volume is given by \(\displaystyle \frac{1}{2}(b_{1}+b_{2})lw\)

\(\displaystyle b_{1}=4, \;\ b_{2}=14, \;\ l=50-(14+14), \;\ w=20\)

Find the other volumes and then add them up. You can fill at a rate of 10 gallons per minute.

Divide 10 into your total to find the minutes needed to fill the whole thing. The easiest thing, may be to subtract off the 6 inches portion.

That is just .5(50)(20)

If you want the time in hours, divide by 60.