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Math Help - Can this be solved?

  1. #1
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    Can this be solved?

    How long did it take Helen to drive from her house to her mother's house?

    1. Her average speed was 72 mph.
    2. If her average speed had been 8 miles per hour greater, it would have taken her 1 hour less.

    The multiple choice answers are (it's a GMAT problem):

    A. Statement 1 is enough, but not statement 2.
    B. Statement 2 is enough, but not statement 1.
    C. Both Statement 1 and 2 are needed to answer this question.
    D. Either statement can be used to answer this question.
    E. Neither statement can be used to answer this question.

    I chose E, but this exam says that the answer is C. I just don't see how this can be solved without a total distance and a time.

    Thanks in advance.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by crazirani View Post
    How long did it take Helen to drive from her house to her mother's house?

    1. Her average speed was 72 mph.
    2. If her average speed had been 8 miles per hour greater, it would have taken her 1 hour less.
    Let the time taken be t, and the distance be d.

    Then condition 1. tells us that::

    d/t=72.

    Note enough information as it stands to find t.

    Condition 2. tells us that the same distance can be covered in 1 hour less time at 80 miles per hour so:

    d/(t-1)=80

    or

    d=80t-80

    Not enough information in this to find t, but with the previous equation we
    have a pair of simultaneaou equations which will allow us to find both d and t.

    from the first equation d=72t. Substitute this into the second:

    72t=80t-80

    rearranging:

    8t=80,

    or t=10 hours

    The multiple choice answers are (it's a GMAT problem):

    A. Statement 1 is enough, but not statement 2.
    B. Statement 2 is enough, but not statement 1.
    C. Both Statement 1 and 2 are needed to answer this question.
    D. Either statement can be used to answer this question.
    E. Neither statement can be used to answer this question.

    I chose E, but this exam says that the answer is C. I just don't see how this can be solved without a total distance and a time.

    Thanks in advance.
    RonL
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  3. #3
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    Brilliant! Thank you.
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