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Math Help - System of 3 equations involving speed, distance and time - stumped!

  1. #1
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    Question System of 3 equations involving speed, distance and time - stumped!

    I have only been able to set up the solution to this problem, but am completely stuck on how to proceed. All help is greatly appreciated.

    The problem:
    A bicyclist averages one speed uphill, one speed on level ground, and one speed downhill. She estimates the following mileage for her thrwe previous rides:

    • 2 miles uphill, 15 miles level, 5 miles downhill - 1.5 hours

    • 6 miles uphill, 9 miles level, 1 miles downhill - 1.4 hours

    • 8 miles uphill, 3 miles level, 8 miles downhill - 1.6 hours


    What were her average speeds uphill, on level ground and downhill?

    My partial solution:
    Using U, L and D for uphill, level and downhill speeds, respectively, here are the set of equations I have set up:

    • 2/U + 15/L + 5/D = 1.5
    • 6/U + 9/L + 1/D = 1.4
    • 8/U + 3/L + 8/D = 1.6


    Assuming this is right, now what?
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  2. #2
    MHF Contributor
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    Re: System of 3 equations involving speed, distance and time - stumped!

    Hey mammothskip.

    Let x = 1/U, y = 1/L and z = 1/D. Doing this you now have a linear system in the form of Ax = b where you have b and you have A.

    Can you now find the inverse of A to get x = A^(-1)*b?
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  3. #3
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    Re: System of 3 equations involving speed, distance and time - stumped!

    Following chiro's simplification rewrite your three equations in x,y,z and solve by elimination.
    Eliminate x from 1 and 2,then 1 and 3 to give two equations in y and z. Eliminate y or z from these two
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