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Math Help - pipes and work done

  1. #1
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    pipes and work done

    An inlet pipe can (by itself) fill an empty tank in two hours and an outlet pipe (by itself) can drain the same tank when full in five hours. If the tank is half full when the valves for both pipes are opened, how long will it take to fill the tank?
    is the answer 1 hour and 40 minutes? i did it in my head so if someone would correct me if it's wrong id appreciate it.
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    Quote Originally Posted by jarny View Post
    An inlet pipe can (by itself) fill an empty tank in two hours and an outlet pipe (by itself) can drain the same tank when full in five hours. If the tank is half full when the valves for both pipes are opened, how long will it take to fill the tank?
    is the answer 1 hour and 40 minutes? i did it in my head so if someone would correct me if it's wrong id appreciate it.
    Let the torture tank containg G gallons.
    By the conditions the inlet takes 2 hours. That means the rate is \frac{G}{2} \frac{\mbox{gallons}}{\mbox{hour}}.

    The outlet takes 5 hours. That means the rate is \frac{G}{5} \frac{\mbox{gallons}}{\mbox{hour}}

    The tank is half full it has \frac{G}{2} \mbox{gallons}. The net gain from the two pipes is
    \frac{G}{2}-\frac{G}{5} gallons per hour.
    Thus, the question is how long does it take for the net chain to reach \frac{G}{2} gallons?
    The answer is, \frac{\frac{G}{2}}{\frac{G}{2}-\frac{G}{5}} hours.
    Combine the denominator,
    \frac{\frac{G}{2}}{\frac{3G}{10}}
    Divide fractions,
    \frac{G}{2}\cdot \frac{10}{3G}=\frac{5}{3} hours. Which is 1 hour and 40 minutes.
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  3. #3
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    Quote Originally Posted by jarny View Post
    An inlet pipe can (by itself) fill an empty tank in two hours and an outlet pipe (by itself) can drain the same tank when full in five hours. If the tank is half full when the valves for both pipes are opened, how long will it take to fill the tank?
    is the answer 1 hour and 40 minutes? i did it in my head so if someone would correct me if it's wrong id appreciate it.
    In one hour, the inlet pipe fills 1/2 the tank.

    In one hour, the outlet pipe drains 1/5 of the tank.

    \frac{1}{2}-\frac{1}{5}=\frac{3}{10}

    So in one hour, the pipes fill 3/10 of the tank. Since the tank is half full to start with, you only need to fill 5/10 of it.

    So: \frac{5}{10}\div \frac{3}{10}=\frac{5}{3}

    So it takes 5/3 hours to fill the tank. Which ends up being 1 hour and 40 minutes, so you're right
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