Calculating the Rate of Water Height Increase in a Filling Swimming Pool

[notsosmartman]

Ok, I've been trying to figure this problem out of an old textbook for a couple days but seem to get nowhere.

"A swimming pool with a rectangular surface 18 meters long and 12 meters wide is being filled at the rate of .80m^3/min. At one end it is 1.0 m deep and at another it is 2.5 m deep, with a constant slope between ends. How fast is the height of the water rising when the depth of water at the deep end is 1.0 m??"

Any suggestions on how to set the problem up? I would like to solve it myself, but would like a starting place!

Thanks, Caleb

 

[Mark44]

Draw a sketch of a side view of the pool. From the side, the pool looks like a trapezoid, with vertical sides of 1 and 2.5 meters, and length 18 meters. If you put in coordinates for the two points at the end of the sloping bottom, you can find the equation of the line that forms the bottom edge of the pool. The volume of water in the pool between the times when the pool is empty and when there are 1.5 meters of water is the area of the triangle cross-section times the width of the pool.

 

[notsosmartman]

Thanks Mark,

But I'm still having difficulty understudying your explanation. Maybe a sketch will help me understand?

Thanks, Caleb.

 

[Mark44]

Yes, probably, but you should draw it. Just draw a sketch of the side view of the pool.

 

[notsosmartman]

HAHA, i have made so many damn sketches on my dry erase board... but yeah i ican post any drawing on here because its a mac and its new to me...

 

[Redbelly98]

Step 1, in any related rates problem, is to identify the two quantities that are to be related.

They pretty much tell us what one of those quantities is when they ask "how fast is the height of the water rising...?" And they strongly hint at what the other is when they say the pool is "being filled at the rate of .80m^3/min".