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Math Help - 37 Year Old Question

  1. #1
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    37 Year Old Question

    If someone could help me with this question it would be much appreciated.

    A man always drives at the same speed. He makes it from A direct to C in 30 minutes; from A through B to C in 35 minutes; and from A through D to C in 40 minutes. How fast does he drive?

    See the attachment for a picture of the problem.

    Thanks
    Attached Thumbnails Attached Thumbnails 37 Year Old Question-math-problem.jpg  
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  3. #3
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    Quote Originally Posted by tary0901 View Post
    If someone could help me with this question it would be much appreciated.

    A man always drives at the same speed. He makes it from A direct to C in 30 minutes; from A through B to C in 35 minutes; and from A through D to C in 40 minutes. How fast does he drive?

    See the attachment for a picture of the problem.

    Thanks
    1. I've found one solution of this problem - but I don't know if there are still other solutions.

    2. I've modified your sketch a little bit (see attachment)

    3. By the definition of speed: speed=\dfrac{distance}{time}<br />
you know:

    A: \dfrac{z}{30}=v<br />
    B: \dfrac{x+10}{35}=v

    C: \dfrac{y+10}{40}=v

    D: x+y>10 \sqrt{2}\approx 14.1

    4. You'll get a system of equations:

    \left| \begin{array}{rcl}\frac z{30} = \frac{x+10}{35} \\ \frac z{30} = \frac{y+10}{40} \\ \frac{y+10}{45} = \frac{x+10}{35} \end{array}\right.

    Solve for (x, y, z).

    I've got \left(\frac76 z-10, \frac43 z -10,z \right)

    5. If - and only if - you use integers for z then the 1st tripel which satisfies the given conditions is \left(\frac{19}3 , \frac{26}3,14  \right). The 1st tripel which consists of integers would be (11, 14, 18)

    6. Depending on the value of z the speed is v = 2 z \ \frac{mi}{h}
    Attached Thumbnails Attached Thumbnails 37 Year Old Question-glgeschwdkt_andererweg.png  
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