Obreros Enfermos: Cálculo Para Cumplir Plazos
Let's dive into a classic workforce problem where a contractor faces unexpected setbacks. This scenario involves calculating how many workers fell ill to ensure a project meets its deadline. It's a practical application of proportional reasoning and resource management, something we encounter in real-world project planning all the time.
El Problema Inicial (The Initial Problem)
The initial setup:
Imagine a contractor, super confident, promising to finish a job in exactly 36 days. To make this happen, they've got 48 workers, each putting in a solid 8 hours every single day. This sounds like a well-oiled machine, right? Everyone's on board, the plan is set, and the deadline seems totally achievable. But, as we all know, things rarely go exactly as planned. This is where things get interesting.
La Interrupción (The Interruption)
After a good 24 days of solid work, disaster strikes! A bunch of workers get sick – maybe it was the office pizza, maybe it was a bad flu season. Whatever the cause, they're out of commission for 6 whole days. This is a serious setback! The project is now behind schedule, and the pressure is on to figure out how to catch up and still meet that original deadline.
El Desafío (The Challenge)
The core question here is: how many workers actually got sick? This isn't just about counting heads; it's about understanding how the reduced workforce impacts the project's timeline and figuring out exactly how many people needed to be out sick to cause the schedule disruption.
This requires careful calculation, understanding work rates, and figuring out how to compensate for the lost time and manpower. It's a bit like a puzzle, and we need to piece together all the information to find the missing number.
Desglosando el Problema (Breaking Down the Problem)
Okay, guys, let's break this down step by step so we can really see what's going on. We need to figure out how much work was supposed to be done, how much actually got done, and how much is left to do with a smaller crew.
Trabajo Total Planificado (Total Planned Work)
First, we need to calculate the total amount of work required for the project. We can measure this in "worker-hours." This tells us the overall scope of the project.
- Workers: 48
- Hours per day: 8
- Days: 36
Total worker-hours = 48 workers * 8 hours/day * 36 days = 13,824 worker-hours. This is our target. This is the total amount of effort needed to complete the project on time.
Trabajo Realizado Antes de la Enfermedad (Work Done Before the Illness)
Next, we calculate how much work was completed before the workers got sick. This is the easy part, because everything was going according to plan.
- Workers: 48
- Hours per day: 8
- Days: 24
Total worker-hours completed = 48 workers * 8 hours/day * 24 days = 9,216 worker-hours. So far, so good. A significant chunk of the project is already done.
Trabajo Restante (Remaining Work)
Now, let's find out how much work is still left to be done after those initial 24 days. We simply subtract the work completed from the total work required.
Remaining worker-hours = 13,824 total worker-hours - 9,216 completed worker-hours = 4,608 worker-hours. This is what we have to finish, and we're under pressure to get it done on time!
Tiempo Restante (Remaining Time)
Crucially, we also need to know how much time we have left to complete this remaining work. Remember, the original deadline is still looming!
Total days: 36 Days worked: 24 Days of illness: 6
Remaining days = 36 total days - 24 days worked - 6 days of illness = 6 days. Yikes! We only have 6 days to finish the job. This is where the rubber meets the road. We're seriously crunched for time.
Calculando los Obreros Necesarios (Calculating the Needed Workers)
Okay, here's where the math gets really interesting. We need to figure out how many workers are required to complete the remaining work in the remaining time.
Obreros Necesarios (Workers Needed)
Let 'x' be the number of workers needed to complete the remaining 4,608 worker-hours in 6 days, working 8 hours per day.
x workers * 8 hours/day * 6 days = 4,608 worker-hours
48x = 4,608
x = 4,608 / 48
x = 96 workers. Wow! We need a total of 96 workers to finish the job on time.
Obreros Adicionales (Additional Workers)
But hold on! We didn't start with zero workers. We already have some workers still on the job. To find out how many additional workers we need, we subtract the number of workers still working from the total number of workers needed.
- Initial workers: 48
- Workers needed: 96
Therefore, the number of workers who got sick is: 96 - 48 = 48 obreros. This means that exactly half the workforce was out sick.
Conclusión (Conclusion)
So, there you have it! To meet the deadline, 48 workers must have been sick and unable to work. This problem highlights how unexpected events can impact project timelines and the importance of careful planning and resource management. It also showcases how mathematical principles can be applied to solve real-world challenges in construction and other industries.
Hopefully, breaking it down step-by-step like this makes the whole process easier to understand. It's all about taking a big problem and turning it into smaller, manageable calculations. Good luck with your own project planning, and try to keep the office pizza healthy!