Question

At sunrise two old women started to walk towards each other. one started from point a and went towards point b while the other started at b and went towards
a. they met at noon but did not stop; each one continued to walk maintaining her speed and direction. the first woman came to the point b at 4:00 pm, and the other one came to point a at 9:00pm. at what time did the sun rise that day?

Answer 1

Let the distance between points a and b = d

For the women starting from a her velocity be $V_1$ and for the women starting from b her velocity be $V_2$

Let the rising time of sun = x AM

We have  $V_1$ = $\frac{d}{12+4-x}$

and we also have  $V_2$ = $\frac{d}{12+9-x}$

At they meet means, they both travel a combined distance of d

So we have   $V_1*(12-x)+V_2*(12-x)=d$

Substituting velocity values we will get

  $\frac{d}{12+4-x}*(12-x)+\frac{d}{12+9-x}*(12-x)=d\\ \\ \frac{12-x}{12+4-x}+\frac{12-x}{12+9-x}=1\\ \\ \frac{12-x}{16-x}+\frac{12-x}{21-x}=1\\ \\ 252-21x-12x+x^2+192-12x-16x+x^2=336-16x-21x+x^2\\ \\ x^2-24x+108=0\\ \\ (x-6)(x-18)=0$

 x= 6 AM or 18 AM, but 18 AM is not possible,

Sun rise time is 6 AM