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Math Help - I have two questions that I don't know how to do.

  1. #1
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    I have two questions that I don't know how to do.

    Could somebody show me step by step what to do?

    1. Two patients in hospital require intravenous fluids. Based on their weights, it's calculated that they need 2 litres and 3 litres, respectively, given at a steady rate over 6 hours. The volume of 1 drop of fluid is 0.05ml. If the first drop of both infusions fall simultaneously at exactly midnight:

    (i) At what time will the two infusions both drop simultaneously again?

    (ii) What is the combined total number of drops that both patients would have received from both infusions when this happens? (Assume that the time it takes for a drop is negligible.)

    Answers. (i) 1.08 seconds
    (ii) 7 drops in total.

    2. Cars A, B and C race from Point 1 to Point 2 and back at constant speeds along an elliptical track. Car A is faster than B and B faster than C. After the start of the race the only time car A and C cross each other, car C has only gone 4/11 of the way from Point 1 to Point 2.

    If car B is moving at three times the speed of car C what fraction of the distance between Point 1 and 2 will car A have covered between passing car B and car C. (Ignore actual bends at both ends of the ellipse which make up a negligible part of the distance from point 1 to point 2.)

    This is pretty much the picture in the book:

    http://img8.imageshack.us/img8/8307/raceb.jpg

    The answer to 2 is 24/55.


    I have no idea where to even begin with either question and the book only has the answers.
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  2. #2
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    For the first one, the patient with the 2L infusion is given the fluid at a rate

    of 50/27 drops per second and the 3L patient at 25/9 drops per second.

    The first one is a rate 2/3 that of the 3L patient.

    The drops will fall at the same time when one gives the 2nd drop and one the 3rd drop.

    \frac{2}{\frac{50}{27}}=\frac{27}{25}=1.08

    \frac{3}{\frac{25}{9}}=\frac{27}{25}=1.08
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