A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and

Discussion in 'Calculator Requests' started by math_celebrity, Jan 8, 2017.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and walked back to the starting point along the same path. She walks 4mph on level ground, 3 mph uphill, and 6 mph downhill. Find the distance she walked.
    Hint: Think about d = rt, which means that t = d/r. Think about each section of her walk, what is the distance and the rate. You know that the total time is 5 hours, so you know the sum of the times from each section must be 5.


    Let Level distance = L and hill distance = H. Add the times it took for each section of the walk:
    L/4 + H /3 + H/6 + L/4 = 5

    The LCD of this is 12 from our LCD Calculator

    Multiply each side through by our LCD of 12
    3L + 4H + 2H + 3L = 60

    Combine like terms:
    6L + 6H = 60

    Divide each side by 3:
    2L + 2H = 20

    The woman walked 20 miles
     

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