more complicated pool problem

[JackL.]

A swimming pool is 50m long and 20 m wide. Its depth decreases linearly along the length from 9 m to 1m. It is initially empty and is filled at a rate of 1m3/min. how fast is the water level rising 360 min after the filling begins? How long will it take to fill the pool?

[mike]

Hi, thanks for posting this problem. Can you tell me what you've tried so far? Or what ideas you have for how to begin?

Mike

[JackL.]

hi
i have tried so far is using the formula v=1/2bh(h for depth).
then i solve for the dv/dt and plugging in all the numbers and i am stuck.

[mike]

I'm going to try to make a video for this but I'm going to be really busy for the next week or 2 and I'm not sure when I'll have time. In the meantime here are some hints:

Try drawing the pool from the side.
Break the drawing up into a rectangle and a triangle.
Use similar triangles to find the volume in terms of height (see the third video in )
Use the volume to find the height after 360 mins
Take the derivative of the volume equation and then afterwords plug in the height you found.


Hope that helps alittle, it's essentially a step by step guide for answering the first part of the question!

Goodluck,
M.

[JackL.]

Cool! thx man!.
i will try my best.