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20 February, 10:53

Two cars left the city for a suburb, 480 km away, at the same time. The speed of one of the cars was 20 km/hour greater than the speed of the other, and that is why it arrived at the suburb 2 hour earlier than the other car. Find the speeds of both cars.

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  1. 20 February, 12:21
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    The speed of both the cars are 80km/h and 60km/h

    Step-by-step explanation:

    Let the speed of one car be 'a' and the speed of other car be 'b'.

    The total distance (d) = 480km

    It is given that the speed of one car is 20km/h faster than the other.

    We can write,

    a = b+20

    The slower car takes 2 hrs more to reach the suburb than the other car.

    Let the time taken by the fastest car be t

    Speed = distance/time

    So,

    a = 480 / t

    b = 480 / (t+2)

    We got the values of a and b.

    a = b+20

    480/t = (480 / (t+2)) + 20

    Taking LCM on the right side.

    480/t = (480 + 20t + 40) / (t+2)

    480 (t+2) = (480+20t+40) t

    480t + 960 = 480t + 20t (t) + 40t

    20t (t) + 40t - 960 = 0

    Divide the whole equation by 20 to simplify the equation.

    t (t) + 2t - 48 = 0

    Solve the quadratic equation by splitting the middle terms.

    t (t) + 8t - 6t - 48 = 0

    t (t + 8) - 6 (t + 8) = 0

    (t - 6) (t+8) = 0

    t = 6 (or) - 8

    t is time and cannot be negative. So t = 6hrs

    a = 480/t

    a = 480 / 6 = 80

    the speed of the fastest car is 80km/hr

    a = b + 20

    b = a - 20

    b = 80 - 20

    b = 60km/h
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