A swimming pool is 50m long and 20m wide. Its depth decreases linearly along the

Question

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 250 min after the filling begins? How long will it take to fill the pool?

My teacher did this example in class and I am completely confused how he takes the slope of the line (25x) and puts it into the equation (B*H*1/2 => (25x)*(x)*1/2 and gets 12.5x^2 * 20 = 250x^2. So the V=250x^2, then d/dt v= 250x^2 is dv/dt = 500x dx/dt and then he gets 1/500 as an answer... I get that dV/dt = 1m^3/min so then I get 1/500x = dx/dt NOT dx/dt = 1/500.... and then like I mentioned before, how does the hypotenuse plug into the b*h*1/2 equation... Thanks in advance

Explanation / Answer

The sloping part of the pool is filled first, followed by the "rectangular" part.
As the sloping part of the pool rises 2m along its 50m length then for a height (h) of water the length is 50h/2 = 25h.
The Sloping Volume = Width x Triangular cross section of water = 20 x

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.