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12 September, 03:44

A car travels 120 miles in the same amount of time that it takes a truck to travel 100 miles. The car travels 10 miles per hour faster than the truck. True or false?

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  1. 12 September, 04:21
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    The affirmation is only true if the truck is traveling at 50 mi/h.

    Explanation:

    Hi there!

    Let's use the equation of average velocity (AV) to solve this problem:

    AV = Δx / t

    Where:

    Δx = traveled distance.

    t = time.

    For the car, its average velocity (vc) will be:

    vc = 120 miles / t

    For the truck:

    vtr = 100 miles / t

    If we solve both equations for t and then equalize them (since the time is the same for both vehicles):

    vc = 120 miles / t

    t = 120 mi / vc

    vtr = 100 miles / t

    t = 100 mi / vtr

    120 mi / vc = 100 mi / vtr

    multiply both sides by vc and divide by 100:

    120 mi / 100 mi = vc / vtr

    1.2 = vc / vtr

    1.2 · vtr = vc

    The car travels 1.2 times faster than the truck.

    Let's see at which velocity of the truck, the car is traveling 10 mi/h faster. In this case, vc = 10 mi/h + vtr:

    1.2 · vtr = 10 mi/h + vtr

    1.2 vtr - vtr = 10 mi/h

    0.2 vtr = 10 mi/h

    vtr = 10 mi/h / 0.2

    vtr = 50 mi/h

    The affirmation is only true if the truck is traveling at 50 mi/h.
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