# Mathematics Blue

posted by .

A person is trying to fill her new swimming pool for the first time. Water is flowing into the pool at a constant rate of 30 liters/min. Unfortunately there is a hole and a crack in the pool from which water is leaking. Water is leaking out of the hole at a rate proportional to the square of the amount of water currently in the pool while water is leaking out of the crack at a rate proportional to the amount of water currently in the pool. As it had rained the previous day, the pool already contained 20 liters of water before filling began. let t(mins) be the time since the person started filling the pool and let W(t) be the number of liters of water in the pool at time t. Write down but do not solve the differential equation for W(t) along with its initial condition.

Now, is this correct?, this is as far as I have gotten but I am not sure if this is right?

I put dw/dt in as 30t, because it is 30 liters/min the rate of flow into the pool.

I put dw/dt out as -kw^2 - pw, because it is the sqaure and the constant amount as the rate of the flow out of the pool.

So combining this, dw/dt is 30t - kw^2 - pw where w(0) = 20 as the initial condition.

IS THIS RIGHT???

Thank you for the help in advance.

## Similar Questions

1. ### physics

Water flows into a swimming pool at a rate of 9.59 gal/min. If the pool dimensions are 30.9 ft wide, 47.6 ft long and 13 ft deep, how long does it take to fill the pool?
2. ### physics

Please help me solve !!! Water flows into a swimming pool at the rate of 9.83 gal/min. If the pool dimensions are 33.4 ft wide, 44.9 ft long and 19.9 ft deep, how long does it take to fill the pool?
3. ### math - calculus

Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 9 cubic feet per minute. If the pool has radius 3 feet and height 11 feet, what is the rate of change of the height …
4. ### calculus

Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 9 cubic feet per minute. If the pool has radius 3 feet and height 11 feet, what is the rate of change of the height …
5. ### Physics

Water flows into a swimming pool at the rate of 5 . 25 gal / min. If the pool dimensions are 33 . 8 ft wide, 40 ft long and 11 . 1 ft deep, how long does it take to fill the pool?
6. ### Math

A swimming pool size is 42 m long and 55 m wide with an average depth of 7.5 m. Using the density of water as 1 g/ml: A. how many gallons of water fill the pool B. The weight of water in lbs after the pool is full C. How long will …
7. ### math

Sarah's parents are filling their swimming pool. She wants to know how long it will take. What unit is best used to give the rate of the water flowing into the pool?
8. ### Calculus

Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 3 cubic feet per minute. If the pool has radius 6 feet and height 10 feet, what is the rate of change of the height …
9. ### Math

Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 3 cubic feet per minute. If the pool has radius 6 feet and height 10 feet, what is the rate of change of the height …
10. ### Math

A swimming pool holds 27460L of water. How long will it take to fill the pool at a rate of 50L/min?

More Similar Questions