No. Two linear equations in three unknowns will always yield many
solutions (or zero solutions). These are essentially plane
equations. Two planes intersect in a line (unless they are
parallel). You might get a de facto unique solution for some values
of Vu, Vd, Vu, T1, T2 from the constraints x,y,z >= 0. It would have
to lie on an axis.
For example, you can aways pick z and find x and y. Using your
notation,
x/Vd + y/Vp + z/Vu = T1
x/Vu + y/Vp + z/Vd = T2
Subtract to get:
x(1/Vd - 1/Vu) + z(1/Vu - 1/Vd) = T1 - T2
then
x = [ (T1 - T2) - z(1/Vu - 1/Vd) ] / (1/Vd - 1/Vu)
So now you can pick any z and get x. Once you have both of these,
plug them in here:
y = Vp (T1 - x/Vd - z/Vu)
As long as x,y,z >= 0, you are in business.
On Sep 14, 10:51 pm, Terence <technic....@gmail.com> wrote:
> You could also get a unique solution if the car has speed of 72 63 56
> in downhill, plain and uphill respectively.
>
> I think the speed Vd, Vp, Vu was chosen so that 2Vp = Vd + Vu.
> But for unique solution, it ought to be 2/Vp = 1/Vd + 1/Vu.
>
> Under this condition, we can get the unique S=x+y+z:
> From
> x/Vd + y/Vp + z/Vu = T1
> x/Vu + y/Vp + z/Vd = T2
> We get (1/Vu+1/Vd)(x+z)+2/Vp*y = T1+T2
> Apply 2/Vp = 1/Vd + 1/Vu, then 2/Vp(x+y+z)=T1+T2
> S=x+y+z = Vp(T1+T2)/2
>
> On 2010-9-15 9:31, Gene wrote:
>
>
>
> > This isn't right. Dropping both y terms is the same as setting y to
> > zero. The answer you get is correct, but there are many others as has
> > been said.
>
> > You could get a unique solution if the route were constrained to be
> > monotonic (level and up or else level and down).
>
> > On Sep 14, 4:28 pm, Minotauraus<anike...@gmail.com> wrote:
> >> Actually the solution is unique. The middle part with the Ys is the
> >> same and therefore can be omitted out. Now you are left with
> >> 2 equations and 2 unknowns.
>
> >> I used time in minutes and I have x = 1.28, z = 0.30476 units (y can
> >> be found out).
>
> >> I guess the trick was 1. to write the equations that Yan did
> >> and 2. to recognize that the plain part is the same and hence can be
> >> cancelled.
>
> >> On Sep 14, 3:31 am, Yan Wang<wangyanadam1...@gmail.com> wrote:
>
> >>> actually, there are many solutions, just pick up one from them...
> >>> On Tue, Sep 14, 2010 at 3:23 AM, Abhilasha jain
> >>> <mail2abhila...@gmail.com> wrote:
> >>>> how can u solve 3 variables using 2 equations?
> >>>> On Tue, Sep 14, 2010 at 3:44 PM, Yan Wang<wangyanadam1...@gmail.com>
> >>>> wrote:
> >>>>> x/72 + y/64 + z/56 = 4
> >>>>> &
> >>>>> x/56 + y/64 + z/72 = 4+2/3
> >>>>> find a solution to this ...
> >>>>> On Tue, Sep 14, 2010 at 2:31 AM, bittu<shashank7andr...@gmail.com>
> >>>>> wrote:
> >>>>>> Amazon Interview Question for Software Engineer / Developers
> >>>>>> A car has speed of 72 64 56 in downhill, plain and uphill
> >>>>>> respectively . A guy travels in the car from Pt. A to pt. B in 4 Hrs
> >>>>>> and pt. B to pt. A in 4 Hrs and 40 min. what is the distance between A
> >>>>>> and B?
> >>>>>> Regards
> >>>>>> Shashank
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