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Math Help - Using Two Pumps

  1. #1
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    Using Two Pumps

    A 5 horsepower (hp) pump can empty a pool in 5 hours. A smaller, 2hp pump empties the same pool in 8 hours. The pumps are used together to begin emptying this pool. After 2 hours, the 2hp pump breaks down. How long will it take the larger pump to empty the pool?

    SIDE QUESTIONS:

    (1) Is this question similar to math questions about working alone and working together?

    (2) How do you set up an equation for such a question?

    I got lost when the 2hp pump broke down after 2 hours.
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  2. #2
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    Quote Originally Posted by symmetry View Post
    A 5 horsepower (hp) pump can empty a pool in 5 hours. A smaller, 2hp pump empties the same pool in 8 hours. The pumps are used together to begin emptying this pool. After 2 hours, the 2hp pump breaks down. How long will it take the larger pump to empty the pool?
    The first pump pumps 1/5 of the pool per hour,

    The second pump pumps 1/8 of the pool per hour.

    Together they pump 1/5+1/8 = 13/40 of the pool per hour.

    In two hours working togethe they have emptied 2*(13/40)=13/20 of the
    pool, leaving 7/20 to be emptied by the first pump alone at 1/5 of the pool
    per hour. So it will take (7/20)/(1/5) hours to finish emptying the pool,
    which is 7/4 hours = 1 hour 45 min.

    SIDE QUESTIONS:

    (1) Is this question similar to math questions about working alone and working together?
    yes

    (2) How do you set up an equation for such a question?
    I do it as shown above.

    RonL
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  3. #3
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    Quote Originally Posted by symmetry View Post
    A 5 horsepower (hp) pump can empty a pool in 5 hours. A smaller, 2hp pump empties the same pool in 8 hours. The pumps are used together to begin emptying this pool. After 2 hours, the 2hp pump breaks down. How long will it take the larger pump to empty the pool?

    SIDE QUESTIONS:

    (1) Is this question similar to math questions about working alone and working together?

    (2) How do you set up an equation for such a question?

    I got lost when the 2hp pump broke down after 2 hours.
    Hello,

    to (1): yes

    to (2):

    let p be the content of the pool.

    the 5hp-pump empties in 1 hour \frac{p}{5} of the content.


    I got lost when the 2hp pump broke down after 2 hours.[/QUOTE]

    Hello,

    to (1): yes

    to (2):

    let p be the content of the pool.

    the 5hp-pump empties in 1 hour \frac{p}{5} of the content.

    the 2hp-pump empties in 1 hour \frac{p}{8} of the content.

    Together and alone after 2 hours:

    \left(\frac{p}{5}+\frac{p}{8} \right)\cdot 2+\frac{p}{5} \cdot x=p

    Divide the equation by p, expand the brackets:
    \frac{13}{20}+\frac{1}{5} \cdot x=1. Solve for x. I've got:
    x = 7/4 hours = 1 h 45 min.

    EB
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