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21 June, 15:03

An automobile travels 280km at a certain speed. If the speed had been 5 km/h faster, the trip would have been made in 1 hour less time. Find the original speed of the automobile.

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  1. 21 June, 15:16
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    If it they travel at the same speed then acceleration will be 0

    Using the equation s = ut + 1/2 a t ^2

    Since a is 0

    S = ut

    From this we can form simultaneous equations

    At Original speed

    280=ut

    Making the time t the subject t = 280/u

    At new speed

    280 = (u+5) (t-1)

    Again making time t the subject

    t = 280 / (u+5) + 1

    Set equations equal to each other

    280/u = 280 / (u+5) + 1

    Get rid of fractions by multiplying everything by denominators (u) (u+5)

    (u) (u+5) (280/u) = (u) (u+5) (280 / (u+5)) + (u) (u+5)

    Cancel terms and simplify to get to

    280 (u+5) = 280u + u (u+5)

    Expand and Solve

    280u + 1400 = 280u + u^2 + 5u

    u^2 + 5u - 1500 = 0

    Factorise

    (u + 40) (u - 35)

    Therefore u = - 40 or 35

    Speed cannot be negative as travelling to a place hence the spited has to be 40km/h
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