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` =
`(d)/(12+4-x)`

and we also have
`V_2` =
`(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

`(d)/(12+4-x)*(12-x)+(d)/(12+9-x)*(12-x)=d\\ \\ (12-x)/(12+4-x)+(12-x)/(12+9-x)=1\\ \\ (12-x)/(16-x)+(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