If 5 men build a wall in 40 days, in how many days will 4 men build the wall?
Understand the Problem
The question is explaining the unitary method, specifically in relation to calculating prices and work done by a group of people. It demonstrates how to find the price of items and how long it takes for different numbers of people to complete a task.
Answer
The time taken by 4 men to build the wall is 50 days.
Answer for screen readers
The time taken by 4 men to build the wall is 50 days.
Steps to Solve
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Identify the total work done The problem states that 5 men can build a wall in 40 days. Therefore, the total work done (in terms of man-days) is calculated as: $$ \text{Total work} = \text{Number of men} \times \text{Number of days} = 5 \times 40 = 200 \text{ man-days} $$
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Calculate work done by 1 man If 5 men can complete the work in 40 days, we can find out how long it would take for 1 man to do the same work: $$ \text{Time taken by 1 man} = \frac{\text{Total work}}{5} = \frac{200}{5} = 40 \text{ days} $$
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Determine time taken by 4 men Next, we calculate how long it will take for 4 men to complete the same amount of work: Using the total work calculated previously, we have: $$ \text{Time taken by 4 men} = \frac{\text{Total work}}{4} = \frac{200}{4} = 50 \text{ days} $$
The time taken by 4 men to build the wall is 50 days.
More Information
This problem illustrates how the unitary method can be used to solve problems related to work and time. It can be applied to various resource allocation situations.
Tips
- Misunderstanding how to distribute work across different numbers of workers.
- Confusing man-days with actual days without proper calculations.
- Forgetting to convert the total work calculated into the necessary format for multiple workers.
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