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Math Help - distance

  1. #1
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    distance

    If a car starts from A towards B with some velocity due to some problem in the engine after traveling 30km.If the car goes with 4/5th of its actual velocity the car reaches B 45min later to the actual time. If the car engine fails after traveling 45km, the car reaches the destination B 36min late to the actual time, what is the initial velocity of car and what is the distance between A and B in km ?

    (a) 40 & 100
    (b) 10 & 150
    (c) 20 & 130
    (d) 50
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  2. #2
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    Quote Originally Posted by sri340 View Post
    If a car starts from A towards B with some velocity due to some problem in the engine after traveling 30km.If the car goes with 4/5th of its actual velocity the car reaches B 45min later to the actual time. If the car engine fails after traveling 45km, the car reaches the destination B 36min late to the actual time, what is the initial velocity of car and what is the distance between A and B in km ?
    1. Let d denote the distance between A and B, v the original speed of the car and t the original traveling time.

    2. According to the text of the question I've got a system of simultaneous equations:

    \left|\begin{array}{rcl}\dfrac dv&=&t \\ \\ \dfrac{30}v + \dfrac{d-30}{0.8 \cdot v} &=& t + \dfrac34 \\ \\ \dfrac{45}v + \dfrac{d-45}{0.8 \cdot v} &=& t+\dfrac35 \end{array}\right.

    3. Unfortunately the solution of this system doesn't match any of the given results so either I didn't understand the question correctly or the given results are wrong ... ?

    My result: (d, t, v)= \left(105,  \frac{21}5,  25 \right)
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