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16 February, 18:23

Two trains leave Cleveland at the same time. One train travels east and the other travels west. The speed of the westbound train is 3mph greater than the speed of the eastbound train. After 3 hours, they are 468 miles apart. Find the rate of each train. Assume that the trains travel in a straight line in directly opposite directions

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  1. 16 February, 19:01
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    The Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.

    Step-by-step explanation:

    1. Let's review all the information provided for solving this question:

    Eastbound train speed = x

    Westbound train speed = x + 3 miles per hour (The speed of the westbound train is 3mph greater than the speed of the eastbound train)

    Duration of trip = 3 hours

    Distance between trains after 3 hours = 468 miles

    2. Let's find the speed of each train, using the following equation:

    3x + 3 (x + 3) = 468

    3x + 3x + 9 = 468

    6x + 9 = 468

    6x = 468 - 9 (Subtracting 9 at both sides)

    6x = 459

    x = 459/6 (Dividing by 6 at both sides)

    x = 76.5 miles per hour

    The Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.

    3. Proof that x = 76.5 is correct

    3x + 3 (x + 3) = 468

    3 (76.5) + 3 (76.5 + 3) = 468

    229.5 + 238.5 = 468

    468 = 468

    The value of x = 76. 5 is correct. And now we know that the Eastbound train has traveled 229.5 miles since the departure from Cleveland and the Westbound train 238.5 miles.
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