# Question #6c523

May 24, 2015

The speed of each chef is:

($r$=recipe)

${v}_{A} = \frac{1 r}{5 h} = 0.2 \frac{r}{h}$,

${v}_{B} = \frac{1 r}{2 h} = 0.5 \frac{r}{h}$,

${v}_{C} = \frac{1 r}{2.5 h} = 0.4 \frac{r}{h}$.

After $x$ hours every chef will do $v \cdot x$ fraction of the recipe.

The three chef together in $x$ hours will do:

$0.2 \frac{r}{h} \cdot x + 0.5 \frac{r}{h} \cdot x + 0.4 \frac{r}{h} \cdot x$.

But we want that the three chefs will do only $1 r$, so:

$0.2 \frac{r}{h} \cdot x + 0.5 \frac{r}{h} \cdot x + 0.4 \frac{r}{h} \cdot x = 1 r \Rightarrow$

$1.1 \frac{r}{h} \cdot x = 1 r \Rightarrow x = 1 r \cdot \frac{1}{1.1} \frac{h}{r} \cong 0.91 h \cong 0.91 \cdot 60 \min \cong 55 \min$.