Results 1 to 4 of 4

Math Help - rate of change, swimming pool

  1. #1
    Newbie
    Joined
    Nov 2011
    Posts
    6

    rate of change, swimming pool

    Swimming pool is 10m long, 6m wide, depth is 1m at one end and 1.5m at the other end.

    It's being filled with water at a rate of 50,000 cm^3 / minute.

    After 225 minutes after the hose is turned on, the water is rising at a rate of _____cm per second.

    Here's what I did:

    dv/dt = 833 1/3 cm^3 / second

    dv/dt = wl(dD/dt)

    wl = 60,000cm

    so dD/dt = dv/dt / 60,000
    dD/dt = (833 1/3) / 60,000

    dD/dt = 0.014 cm/sec for the answer.

    Does the 225 minutes even come into play? I'm thinking it would since the depth isn't constant?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Re: rate of change, swimming pool

    Quote Originally Posted by stefanhinote View Post
    Swimming pool is 10m long, 6m wide, depth is 1m at one end and 1.5m at the other end.

    It's being filled with water at a rate of 50,000 cm^3 / minute.

    After 225 minutes after the hose is turned on, the water is rising at a rate of _____cm per second.

    Here's what I did:

    dv/dt = 833 1/3 cm^3 / second

    dv/dt = wl(dD/dt)

    wl = 60,000cm

    so dD/dt = dv/dt / 60,000
    dD/dt = (833 1/3) / 60,000

    dD/dt = 0.014 cm/sec for the answer.

    Does the 225 minutes even come into play? I'm thinking it would since the depth isn't constant?
    Some care must be taken as the volume of the pool is a piecewise defined function

    V=\begin{cases}30h, \quad 0 \le h \le .5 \\ 15+60h, \quad h > .5 \end{cases}

    This happens becuase the bottom of the pool is NOT flat.

    so when you take the derivative you get that

    \frac{dV}{dt}=\begin{cases}30 \frac{dh}{dt}, \quad 0 < h < .5 \\ 60 \frac{dh}{dt}, \quad h > .5 \end{cases}

    You need to use the 225 seconds so you know which one of the above to use.

    Draw a diagram to help illustrate this point.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2011
    Posts
    6

    Re: rate of change, swimming pool

    Thank you, makes more sense now.

    Greetings from Tucson
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,061
    Thanks
    900

    Re: rate of change, swimming pool

    Quote Originally Posted by stefanhinote View Post
    Swimming pool is 10m long, 6m wide, depth is 1m at one end and 1.5m at the other end.

    It's being filled with water at a rate of 50,000 cm^3 / minute.

    After 225 minutes after the hose is turned on, the water is rising at a rate of _____cm per second.

    Here's what I did:

    dv/dt = 833 1/3 cm^3 / second

    dv/dt = wl(dD/dt)

    wl = 60,000cm

    so dD/dt = dv/dt / 60,000
    dD/dt = (833 1/3) / 60,000

    dD/dt = 0.014 cm/sec for the answer.

    Does the 225 minutes even come into play? I'm thinking it would since the depth isn't constant?
    10^6 cm^3 = 1 m^3

    (50000 cm^3/min)(225 min) = 11.25 m^3

    the lower section of the pool (the triangular prism) has a volume of

    V = (0.5 m)(5 m)(6 m) = 15 m^3

    so, the water level has not reached the 0.5 m mark at the deep end yet. dh/dt is variable until it reaches that point, then the water level rises at a constant rate.

    you'll need to get the volume of water in the pool below that point as a function of depth at the deep end, then take the time derivative.
    Attached Thumbnails Attached Thumbnails rate of change, swimming pool-pool.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A circular pool of liquid (rate of change)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 24th 2010, 03:27 PM
  2. swimming pool problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 11th 2010, 11:03 PM
  3. swimming pool problem
    Posted in the Geometry Forum
    Replies: 2
    Last Post: November 22nd 2009, 04:29 AM
  4. Rectangular Swimming Pool
    Posted in the Geometry Forum
    Replies: 4
    Last Post: December 5th 2008, 01:26 PM
  5. Swimming Pool Border
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: January 13th 2007, 02:45 PM

Search Tags


/mathhelpforum @mathhelpforum