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Math Help - A couple more System of Equation problems that are stumping me!

  1. #1
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    A couple more System of Equation problems that are stumping me!

    This one I have tried 3 times, and still can not come up with a answer.

    A manufacturing plant is going to use two different stamping machines to complete an order of 975 units. One produces 100 units per hour, while the other produces 75 units per hour. How long must each machine operate to complete the order if the faster machine needs to be shut down for two and one half hours for repairs?


    Another one that is giving me fits is the following:

    2 Cars are to start at the same place in Knoxville and travel in opposite directions. (Assume they drive in a straight line) The drivers know that one driver drives an average of 5mph faster than the other . They have agreed to stop and call each other after driving for 3 hours. In the telephone conversations they realize that they are 355 miles apart. What was the average speed of each driver?
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  2. #2
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    Hello!

    I'll try the first question.

    During the 2 and a half hours when the faster machine has to be shut down, only the slower machine is operating. Within this 2.5 hours, the slower machine produces 75 x 2.5 = 187.5 units.

    When both machines can work together, we still have 975 - 187.5 = 787.5 units more to produce.

    As mentioned in the question, 1 machine produces 100 units per hour while the other produces 75 per hour. Hence, in 1 hour, with both machines operating, 100 + 75 = 175 units are produced.

    So, how many hours are required to produce the remaining 787.5 units? Take 787.5 / 175 = 4.5 hours.

    Therefore, the slower machine has to operate for 2.5 + 4.5 = 7 hours, while the faster machine has to operate for 4.5 hours to produce all 975 units.

    Hope this helps!
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  3. #3
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    The second one can be solved with algebra...


    Let the average speed of one driver be x mph. The average speed of the faster driver = (x + 5) mph.

    In one hour, the distance between the 2 drivers would be x + (x+5) miles.
    In 2 hours, the distance between the 2 drivers would be x + x + (x+5) + (x+5) miles, or 2 [x + (x+5)] miles
    In 3 hours, the distance between the 2 drivers would be indicated by
    3 [x + (x+5)] miles.

    Through their phone conversations, we can infer that
    3 [x + (x+5)] miles = 355 miles
    Expanding the algebraic expression on the left side, we get
    3x + 3x + 15 = 355
    6x + 15 = 355
    6x = 355 - 15 = 340
    x = speed of the slower driver = 340/6 = 56\frac{2}{3}mph

    Evaluate x + 5 to get speed of the faster driver.

    Hope this helps!
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