Please help this desperate AP Calc student with a related rates problem!!!

[alwaysthefangirl]

Here is the problem:

A swimming pool is 15 feet wide, 8 feet long, and 5 feet deep at one end. The depth gradually decreases to 0 at the other end (as shown in the picture). Water is being added to the pool at the rate of 10 cubic feet per minute. Find the rate at which the water level is rising when there are 300 cubic feet of water in the pool. Hint, think similar triangles and a triangular prism of water.

I am so lost on where to start with this, but here is what I have:

- V(of the water)=(1/2)(l*w*h)
- I think V'(of the water)=10
- I think that V of the water at the end is 300
- V(of the swimming pool)=600

I really dont have anything else
I usually am ok with related rates, but this one makes absolutly no senseeeeeeeeee. Please help!!!!!!

 

[Deleted member 4993]

Here is the problem:

A swimming pool is 15 feet wide, 8 feet long, and 5 feet deep at one end. The depth gradually decreases to 0 at the other end (as shown in the picture). Water is being added to the pool at the rate of 10 cubic feet per minute. Find the rate at which the water level is rising when there are 300 cubic feet of water in the pool. Hint, think similar triangles and a triangular prism of water.

I am so lost on where to start with this, but here is what I have:

- V(of the water)=(1/2)(l*w*h)
- I think V'(of the water)=10
- I think that V of the water at the end is 300
- V(of the swimming pool)=600

I really dont have anything else
I usually am ok with related rates, but this one makes absolutly no senseeeeeeeeee. Please help!!!!!!

Suppose the pool had constant depth - would you be able to solve a similar problem?

Please solve the following:

A swimming pool is 15 feet wide, 8 feet long, and 5 feet deep (constant). Water is being added to the pool at the rate of 10 cubic feet per minute. Find the rate at which the water level is rising when there are 300 cubic feet of water in the pool.

We can extrapolate from this simpler problem. The "governing principle will be same.

 

[skeeter]

I assume a side view of the pool looks like the top diagram, although it could look like the bottom one since quoted 15 ft wide and 8 ft long. You have the advantage of having a given diagram.
Anyway ... see the similar triangles?

 

[Steven G]

How did you get V(of the swimming pool)=600? Try again

You want h' when h = 10

You have, as skeeter points out, 8/5 = l/h or l = 8h/5 ( and w = 15).

V(of the water)=(1/2)(l*w*h) (1/2)( 8h/5 * 15 * h)

Continue ....