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    A runner took part in a 30km road race. He ran the first 17km at an average speed of x kmh^-1. He ran the last 13 km at an average speed of x-2 kmh^-1. The total time to complete the race was 4 hours.

    a. Show that 2x^2 -19x +17 = 0

    b. Hence find his average speed for the first 17km.
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    (Original post by YourGoddamnRight)
    A runner took part in a 30km road race. He ran the first 17km at an average speed of x kmh^-1. He ran the last 13 km at an average speed of x-2 kmh^-1. The total time to complete the race was 4 hours.

    a. Show that 2x^2 -19x +17 = 0

    b. Hence find his average speed for the first 17km.
    The key to this is that the sum of the times for the 17km and 13km sections must be 4 hours. You can find an expression for the time taken for each section from v = s/t rearranged as t = s/v, where t = time, s = displacement and v = velocity. The sum of the two times will be an algebraic expression involving (x) and (x - 2) which you will need to rearrange to the given quadratic equation.

    Part (b) involves solving the quadratic equation for x, discarding the "nonsense" solution. You can do part (b) even if you can't complete part (a).
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    (Original post by old_engineer)
    The key to this is that the sum of the times for the 17km and 13km sections must be 4 hours. You can find an expression for the time taken for each section from v = s/t rearranged as t = s/v, where t = time, s = displacement and v = velocity. The sum of the two times will be an algebraic expression involving (x) and (x - 2) which you will need to rearrange to the given quadratic equation.

    Part (b) involves solving the quadratic equation for x, discarding the "nonsense" solution. You can do part (b) even if you can't complete part (a).
    Thanks for the effort. I happened to hand my paper in before your response.

    But I did write what you've written, on the paper.
 
 
 
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