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1 July, 07:41

Car A, traveling at a constant 10 m/s, crosses the start line 3 seconds before Car B, who is traveling at a constant 15 m/s. At what time and distance, respectively, will the two cars be at the same distance from the start line?

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  1. 1 July, 07:45
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    The distance between Car A and car B, When Car A crosses the start line is:

    distance = speed car B * time

    distance = (15 m/s) (3 s) = 45 m

    Distance traveled by car A = x, (when the car B is at the same distance from the start line)

    time of car A=t

    x=10 m/st ⇒ x=10t (1)

    Distance traveled by car B=x

    time of car B=t-3

    x=15 (t-3) (2)

    With the equations (1) and (2) we make a system of equations:

    x=10t

    x=15 (t-3)

    We solve this system of equations:

    10t=15 (t-3)

    10t=15t-45

    -5t=-45

    t=-45 / - 5

    t=9

    t-3=9-3=6

    x=10 t=10 (9) = 90

    Answer: The time would be 9 seconds for Car A and 6 seconds for car B and the distance would be 90 meters.
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