Slide from Class 45 of the 2024 CML preparation series, presenting a rate problem with 16 workers completing half a job in three-fourths of a day.

It looks like you've uploaded a slide from a CML (Continental Mathematics League) 2024 Preparation class, specifically Class #45, which presents a work-rate problem. Let's solve it step by step.

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🔍 Problem Statement (from the table):

We are given:

| Workers | Days | Job |
|--------|----------|-------|
| 16 | 3/4 | 1/2 |

This means:
16 workers can complete half a job in 3/4 of a day.

We are likely being asked to find out how long it would take a different number of workers to complete a full job, or perhaps determine the rate of work per worker — but since no specific question is stated, we'll infer the most common type of problem: "How many days would it take for a different number of workers to complete a full job?"

But let’s first find the rate of work per worker per day.

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✔ Step 1: Find the total work done

Let’s define:
- Work = Job
- We are told that 16 workers complete ½ job in ¾ day.

So, total work done = ½ job.

Let’s find the combined work rate of 16 workers.

> Work Rate = Work / Time
> So, 16 workers' combined rate = (½ job) / (¾ day) =
> $$
> \frac{1/2}{3/4} = \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3} \text{ jobs per day}
> $$

So, 16 workers together can do 2/3 of a job per day.

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✔ Step 2: Find individual worker’s rate

Now divide by 16 to get one worker’s rate:

$$
\frac{2/3}{16} = \frac{2}{3} \times \frac{1}{16} = \frac{2}{48} = \frac{1}{24} \text{ jobs per day per worker}
$$

So, each worker does 1/24 of a job per day.

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✔ Step 3: Use this to answer a typical follow-up question

Let’s suppose the actual question is:
👉 *"How many days will it take 24 workers to complete 1 full job?"*

(Or maybe: *"How many workers are needed to finish the full job in 1 day?"* — but without a stated question, we’ll assume a common variant.)

Let’s assume the question is:
> How many days will it take 24 workers to complete 1 full job?

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✔ Step 4: Compute rate for 24 workers

Each worker does $ \frac{1}{24} $ job/day →
24 workers do:
$$
24 \times \frac{1}{24} = 1 \text{ job per day}
$$

So, they complete 1 full job in 1 day.

✔ Answer: 1 day

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Alternatively, if the question was:
> "How many workers are needed to complete 1 full job in 1 day?"

Then:
We need total rate = 1 job/day
Each worker contributes $ \frac{1}{24} $ job/day
So number of workers needed:
$$
\frac{1}{1/24} = 24 \text{ workers}
$$

Again, same result.

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🧠 Final Insight:

The key idea is to find the work rate per worker per day, then scale accordingly.

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✔ Summary:

From the data:
- 16 workers → ¾ day → ½ job
- So, each worker’s rate = $ \frac{1}{24} $ job/day

Therefore:
- 24 workers → $ 24 \times \frac{1}{24} = 1 $ job/day → 1 day to complete 1 job
- Or, to complete 1 job in 1 day, you need 24 workers

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💡 If you have a specific question (e.g., “How many days for 8 workers to finish 1 job?”), just let me know and I’ll compute it!

But based on the image and typical CML problems, the most likely intended answer is:

> ✔ It takes 24 workers 1 day to complete 1 full job.

Or conversely, 24 workers are needed to complete the job in 1 day.

Let me know if you'd like to explore other variations!