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Math Help - Find average velocity without a given time or distance??

  1. #1
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    Find average velocity without a given time or distance??

    A family travels from hither to yon one afternoon. On this day, the driver spends half the distance traveling at 77 km/hr and the remaining half at 50 km/hr. What is the average speed of the car during the trip?

    To work the problem, I assumed the trip took 2 hrs, then found how much time was spent at each speed, then found a weighted average of 63.5 km/hr. This is incorrect.

    Someone told me I can't assume the time it took to make the trip. Why not? Half is half, and the proportions will be the same..


    How do I approach the problem?
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  2. #2
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    Re: Find average velocity without a given time or distance??

    Quote Originally Posted by OneMileCrash View Post
    A family travels from hither to yon one afternoon. On this day, the driver spends half the distance traveling at 77 km/hr and the remaining half at 50 km/hr. What is the average speed of the car during the trip?

    To work the problem, I assumed the trip took 2 hrs, then found how much time was spent at each speed, then found a weighted average of 63.5 km/hr. This is incorrect.

    Someone told me I can't assume the time it took to make the trip. Why not? Half is half, and the proportions will be the same..


    How do I approach the problem?
    (speed)(time) = distance, time = (distance)/(speed)

    distance d/2 covered at 77 km/hr ... time = (d/2)/77

    distance d/2 covered at 50 km/hr ... time = (d/2)/50

    total time = d/154 + d/100

    average speed = (total distance)/(total time) = d/(d/154 + d/100) = 1/(1/154 + 1/100) = 7700/127 km/hr
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  3. #3
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    Re: Find average velocity without a given time or distance??

    Gotcha, thanks!
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