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Math Help - Quadratic Equations: Word Problems

  1. #1
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    Quadratic Equations: Word Problems

    "A trip of 720 km is travelled by car. On the return trip, the speed is increased by 10 km/h. The total time spewnt travelling was 17 h. Find the speed each way."
    The answer is 80 km/h and 90 km/h, but I have no idea how to get there. In other words, I can't come up with the right equation to start things off.

    Thanks in advance,

    Sunlis
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  2. #2
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    Quote Originally Posted by Sunlis View Post
    "A trip of 720 km is travelled by car. On the return trip, the speed is increased by 10 km/h. The total time spewnt travelling was 17 h. Find the speed each way."
    The answer is 80 km/h and 90 km/h, but I have no idea how to get there. In other words, I can't come up with the right equation to start things off.

    Thanks in advance,

    Sunlis
    We know that the total travel time is T = 17 h. I am going to set T = t_1 + t_2 where the two t's are for the time out and the time back respectively.

    Each portion of the trip (out and back) was 720 km.

    So
    v_1 = \frac{720 \, km}{t_1}

    v_2 = \frac{720 \, km}{t_2}

    and we know that v_2 = v_1 + 10 \, km/h

    Thus
    t_1 = \frac{720 \, km}{v_1}

    t_2 = \frac{720 \, km}{v_1 + 10 \, km/h}

    Finally we have t_1 + t_2 = 17 \, h

    Thus
    \frac{720 \, km}{v_1} + \frac{720 \, km}{v_1 + 10 \, km/h} = 17 \, h

    I leave solving this to you. I get v_1 = 80 \, km/h as advertised. (Note: You may discard the negative solution as unphysical.)

    -Dan
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  3. #3
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    Awesome.
    For some reason I just couldn't get myself to think properly for that one.
    Thanks for the quick reply.

    Sunlis
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