Cake This is a e-olymp programming question mathematical optimization.
In honor of the birth of an heir Tutti royal chef has prepared a huge cake, that was put on the table for Three Fat Man. The first fat man can eat the cake by himself for t1 hours, second - for t2 hours, and the third - for t3 hours.
For what time can the cake be eaten simultaneously by all three fat men?
I had used this formula. But it is giving wrong answer.
ans=((t1/3.0)+(t2/3.0)+(t3/3.0))/3.0
Please anyone help me.
t1 hours/cake = $\frac{1}{t1}$ cakes/hour.
For all three, they eat $\frac1{t1} + \frac1{t2} + \frac1{t3}$ cakes in one hour.
In h hours, they eat $h(\frac1{t1} + \frac1{t2} + \frac1{t3})$ cakes.
The time to eat a whole cake must satisfy $h(\frac1{t1} + \frac1{t2} + \frac1{t3})=1$ or $h = \frac1{\frac1{t1} + \frac1{t2} + \frac1{t3}}$.
The "eating speeds" are given in hours per cake. It would be better if they were given in cakes per hour (and man) cause speeds in cakes/hour are additive.
