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21 March, 14:34

In a 5.00 km race, one runner runs at a steady 11.4 km/h and another runs at 14.7 km/h. How long does the faster runner have to wait at the finish line to see the slower runner cross?

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  1. 21 March, 15:59
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    0.0986 h or 5 minutes 55 seconds.

    Explanation:

    Speed: This can be defined as the rate of change of distance of a body. The S. I unit of speed is m/s. Speed is a scalar quantity, because it can only be represented by magnitude alone.

    Mathematically,

    Speed = distance/time.

    S = d/t ... Equation 1

    making t the subject of the equation

    t = d/S ... Equation 2

    Form the question,

    Time taken for the faster runner to reach the finish line

    t₁ = d/S₁ ... Equation 3

    Where t₁ = time taken for the faster runner to reach the finish line, d = distance, S₁ = speed of the faster runner.

    Given: d = 5.0 km, S₁ = 14.7 km/h.

    Substituting into equation 3

    t₁ = 5/14.7

    t₁ = 0.340 h

    Also,

    t₂ = d/S₂ ... Equation 4

    Where t₂ = time taken for the slower runner to reached the finished line, d = distance, S₂ = speed of the slower runner.

    Given: d = 5 km, S₂ = 11.4 km/h.

    Substitute into equation 4,

    t₂ = 5/11.4

    t₂ = 0.4386 h.

    The time the faster runner have to wait at the finish line to see the slower runner cross = t₂ - t₁ = 0.4386-0.340

    The time the faster runner have to wait at the finish line to see the slower runner cross = 0.0986 h = 5 mins 55 s.
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