To solve this problem, we need to break it down into two main parts.

Given Information

1. Tom's time to fill an order: $s$ minutes.

2. Paco's time to fill an order: $s - 2$ minutes.

3. Carl's time to fill an order: $s + 1$ minutes.

4. Combined work rates:

   • Tom and Paco: They take 1 minute and 20 seconds (or 1.33 minutes) together to fill an order.
   • Paco and Carl: They take 1 minute and 30 seconds (or 1.5 minutes) together to fill an order.

a) Find $s$: How long does each person take to fill an order?

Let's denote each person's work rate as follows:

• Tom's rate: $\frac{1}{s}$ orders per minute.
• Paco's rate: $\frac{1}{s - 2}$ orders per minute.
• Carl's rate: $\frac{1}{s + 1}$ orders per minute.

Since Tom and Paco together take 1.33 minutes to fill one order, their combined rate is:

$\frac{1}{s} + \frac{1}{s - 2} = \frac{1}{1.33}$

Similarly, since Paco and Carl together take 1.5 minutes to fill one order, their combined rate is:

$\frac{1}{s - 2} + \frac{1}{s + 1} = \frac{1}{1.5}$

We can solve these equations to find the value of $s$.

b) How long would all three of them, working together, take to fill an order?

Once we know $s$, we can calculate the combined work rate of all three:

$\frac{1}{s} + \frac{1}{s - 2} + \frac{1}{s + 1}$

The total time for them to fill one order together would be the reciprocal of this combined rate.

I'll proceed with the calculations and provide the solution.It appears there were no solutions found using the equations as they are, which suggests that an adjustment may be necessary in the approach. This type of problem often requires a careful setup of simultaneous equations or alternative assumptions.

To ensure accuracy, I will double-check the formulation and re-evaluate the approach by examining the equations in terms of possible simplifications or alternative methods. I'll proceed with that.The approach using the given setup still results in no solutions, which suggests a deeper look into either the equations' compatibility or any additional assumptions needed.

Would you like me to explore an alternative approach to approximate the solution or make adjustments based on possible real-world estimations?