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Math Help - Distance

  1. #1
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    Distance

    Some friends on a hike leave at 9a.m. and return at 2p.m. They spend one-quarter of the total distance walking uphill, one-half walking on level ground, and one-quarter walking downhill. If their speed is 4 mph on level ground, 2 mph uphill, and 6 mph downhill, approximately how far did they walk? I came to the answer of 20 miles. Is this correct? Thanks
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  2. #2
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    Hello, jarny

    Some friends on a hike leave at 9 a.m. and return at 2 p.m.
    They spent one-quarter of the total distance walking uphill at 2 mph,
    one-half walking on level ground at 4 mph,
    and one-quarter walking downhill at 6 mph.
    How far did they walk?
    Formula: .Distance .= .Speed x Time . ---> . T = D S

    Let x = total distance.


    They walked x miles uphill at 2 mph. .This took: x 2 = x/8 hours.

    They walked x miles level at 4 mph. .This took: x 4 = x/8 hours.

    They walked x miles downhill at 6 mph. .This took: x 6 = x/24 hours.


    The total time was 5 hours: . x/8 + x/8 + x/24 .= .5

    Multiply by 24: .3x + 3x + x .= .120 . ---> . 7x .= .120


    Therefore, the distance is: . x .= .120/7 miles.

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