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2 December, 21:35

two cars are traveling down the highway with the same speed. if the first car increases its speed by 1 km per hour and the other car decreases its speed by 10 km per hour then the first car will cover the same distance in 2 hours as a second car in 3 hours what is the speed of the cars

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  1. 2 December, 22:02
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    Original speed = 32 km/h

    First car's new speed = 33 km/h

    Second car's new speed = 22 km/h

    Step-by-step explanation:

    "two cars are traveling down the highway with the same speed"

    Let the original speed of both cars be x.

    "the first car increases its speed by 1 km per hour"

    Now its speed is x + 1.

    "the other car decreases its speed by 10 km per hour"

    Now its speed is x - 10.

    Now we need a relationship between speed, distance, and speed.

    speed = distance/time

    Multiply both sides by time and switch sides.

    distance = speed * time

    In 2 hours, the first car covers (speed * time for first car):

    distance = 2 * (x + 1)

    In 3 hours, the second car covers (speed * time for second car)

    distance = 3 * (x - 10)

    The distances are equal, so we set them equal and solve the equation for x.

    2 (x + 1) = 3 (x - 10)

    2x + 2 = 3x - 30

    2 = x - 30

    32 = x

    x = 32

    The original speed of the cars was 32 km/h

    After the speeds changed, the first car's speed is

    x + 1 = 32 + 1 = 33 km/h

    The second car's speed becomes

    x - 10 = 32 - 10 = 22 km/h

    Let's check:

    In 2 hours, the first car covers 2 h * 33 km/h = 66 km

    In 3 hours, the second car covers 3 h * 22 km/h = 66 km

    The distances are the same, so our answer is correct.
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