# Related rates fill rate problem

## Homework Statement

A swimming pool is 50m long and 20m wide. Its depth decreases linearly along the length from 3m to 1m. It is initially empty and is filled at a rate of 1m^3/min. How fast is the water level rising 90 minutes after the filling began?

## The Attempt at a Solution

I'm really lost on this problem, so my attempt at a solution isn't much of one. I assume that I will be using two separate volume formulas: one for the area with the sloped bottom, and one for the rectangle above that. Beyond that I'm lost.

## The Attempt at a Solution

But until the water has covered the bottom, its figure, on the side of the pool will be a right triangle with height x, the height of the water, and base determined by where the line giving the bottom crosses that height. Taking the origin of a coordinate system at the lowest point in the pool, positive x-axis up, The bottom of the pool is the line from (0, 0) to (2, 50). That has equation y= 25x. So the area of the side covered by water will be $(1/2)(25x)(x)= (25/2)x^2$. The volume will be $(25/2)x^2(20)= 250x^2$. That will be true for x, the height of the water, from 0 to 2. After that, it will be the total volume of the water, $250(4)= 1000$, plus the volume of the rectangular solid above it, (20)(50)(x- 2).