Let the contributions of the first, second and third worker per a time unit be $x, y, z$, measured as percentages of the whole work. One half of the work would be done by the second and third worker together within $\frac{1}{2(y+z)}$ time units, by the third and first worker together within $\frac{1}{2(z+x)}$ time units and, by the first and second worker together, within $\frac{1}{2(x+y)}$ time units. By working in the way described in the problem text, they spend $\frac{1}{2(y+z)} + \frac{1}{2(z+x)} + \frac{1}{2(x+y)}$ time units, but if they worked all together, they would spend $\frac{1}{x+y+z}$ time units. We are asked the ratio of these numbers. Since by assumption $\frac{x}{2(y+z)} + \frac{y}{2(x+z)} + \frac{z}{2(x+y)} = 1$, we get
$$\begin{aligned} \frac{\frac{1}{2(y+z)} + \frac{1}{2(z+x)} + \frac{1}{2(x+y)} }{\frac{1}{x+y+z}} &= \frac{x+y+z}{2(y+z)} + \frac{x+y+z}{2(z+x)} + \frac{x+y+z}{2(x+y)} = \\ &= \frac{1}{2} + \frac{x}{2(y+z)} + \frac{1}{2} + \frac{y}{2(z+x)} + \frac{1}{2} + \frac{z}{2(x+y)} = \frac{3}{2} + 1 = 2.5. \end{aligned}$$

Suppose that the first worker worked $a$ time units, the second worker worked $b$ time units and the third worker worked $c$ time units. Altogether, they spend $a+b+c$ time units to perform the whole work. If the second worker worked $a$ time units and the third also $a$ time units, they would perform half of the work. Similarly, if the third worker worked $b$ time units and the first also $b$ time units then they would complete half of the work, and if the first worker worked $c$ time units and the second also $c$ time units, they would complete half of the work. Consequently, if the first worker worked $b+c$ time units, the second worker worked $a+c$ time units and the third worked $a+b$ time units, they would complete one and a half such works. Including the work really done, it turns out that if all workers worked $a+b+c$ time units then they would perform 2.5 such works. Thus the three workers together would act 2.5 times faster than in the situation of the problem.