It takes four workers four and a half days to build a little bridge over a stream.How long would it take two workers to build the same bridge at the same rate?

1. Break Down the Problem

To find out how long it would take two workers to build the bridge, we first need to establish the total work done, which can be measured in worker-days.

2. Relevant Concepts

The total work can be given in terms of "worker-days", which is the product of the number of workers and the number of days they work. If we denote the number of workers as $W$ and the number of days as $D$, the total work can be represented as: $\text{Total Work} = W \times D$

3. Analysis and Detail

Given that:

• $W = 4$ workers,
• $D = 4.5$ days,

The total work in worker-days is: $\text{Total Work} = 4 \text{ workers} \times 4.5 \text{ days} = 18 \text{ worker-days}$

Now we need to find out how many days $D'$ it would take for 2 workers to complete the same amount of work. We can set up the equation: $\text{Total Work} = 2 \text{ workers} \times D' \text{ days}$ Thus: $18 = 2 \times D'$ Solving for $D'$: $D' = \frac{18}{2} = 9 \text{ days}$

4. Verify and Summarize

After performing the calculations, we find that it will take 2 workers 9 days to build the same bridge, confirming our analysis.

Final Answer

It would take two workers 9 days to build the same bridge.