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Math Help - Ratio

  1. #1
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    Ratio

    Can you guys help me answer this question? It's been far too long since I've done ratios.

    "Drain A will empty a tank in 5 hours. Drain B will empty the tank in 6 hours. How long will it take to empty the tank using both drains?"

    And

    "30 min : q min = 6 days : 2 weeks"
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  2. #2
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    Let t be the number of hours needed for A and B to drain the tank.

    1/5=part drained by A in 1 hr.

    1/6=part drained by B in 1 hr.

    1/t=part drained by both in 1 hr.

    1/5+1/6=1/t, solve for t
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  3. #3
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    Hmm... but they don't drain a part of the tank. They drain the whole tank in 5 or 6 hours.
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  4. #4
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    Quote Originally Posted by Rocher View Post
    Can you guys help me answer this question? It's been far too long since I've done ratios....
    And

    "30 min : q min = 6 days : 2 weeks"
    Hello, Rocher,

    rewrite this proportion:

    \frac{30\text{ min}}{q\text{ min}}=\frac{6\text{ days}}{14\text{ days}}. The units cancel out.
    Multiply by q and by 14 and you'll get:

    30 \cdot 14=6 \cdot q. Solve for q

    (For confirmation only: 70)

    EB
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  5. #5
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    Ty!! I just need help on the first question now :P
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  6. #6
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    Quote Originally Posted by Rocher View Post
    ...

    "Drain A will empty a tank in 5 hours. Drain B will empty the tank in 6 hours. How long will it take to empty the tank using both drains?"
    ...
    Hell, Rocher,

    galactus has demonstrated what you should calculate. I'll add a few steps so it could be easier for you to understand:

    1. contents of the tank: T
    2. part of the content which is drained by A in 1 hour: 1/5*T
    3. part of the content which is drained by B in 1 hour: 1/6*T

    4. part of the content which is drained by A and by B together in 1 hour: 1/5*T + 1/6*T

    5. Both pipes need t hours to drain the tank completly:

    t \cdot \left(\frac{1}{5} \cdot T+\frac{1}{6} \cdot T \right) = T. simplify the LHS:

    t \cdot \frac{11}{30} \cdot T = T. Divide by T and then solve for t:
    t=\frac{30}{11}\text{ h}\approx 2.72\ h

    To be exact the time is: 2 h; 43 min; 38.18 s

    EB
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  7. #7
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    You own =) I'm done my homework!! :P
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