1. 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

2. What ideas have you had so far?

3. Originally Posted by tary0901
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: $\displaystyle speed=\dfrac{distance}{time}$ you know:

A: $\displaystyle \dfrac{z}{30}=v$
B: $\displaystyle \dfrac{x+10}{35}=v$

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

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

4. You'll get a system of equations:

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

Solve for (x, y, z).

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

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

6. Depending on the value of z the speed is $\displaystyle v = 2 z \ \frac{mi}{h}$