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Third question. A statue was planned to be built by 40 people and completed in 15 days. If it were to be completed 3 days earlier, how/ many more pecple would you need?

Third question. A statue was planned to be built by $40$ people and completed in $15$ days. If it were to be completed $3$ days earlier, how/ many more pecple would you need?

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Time and work rate problems

Full solution

Q. Third question. A statue was planned to be built by

40

people and completed in

15

days. If it were to be completed

3

days earlier, how/ many more pecple would you need?

Calculate Total Work: Calculate the total amount of work required to build the statue in person-days. $\newline$ Total work $= \text{Number of people} \times \text{Number of days}$ $\newline$ Total work $= 40 \text{ people} \times 15 \text{ days}$ $\newline$ Total work $= 600 \text{ person-days}$
Calculate New Deadline: Calculate the new deadline for the project to be completed $3$ days earlier. $\newline$ New deadline $=$ Original number of days $-$ $3$ days $\newline$ New deadline $=$ $15$ days $-$ $3$ days $\newline$ New deadline $=$ $12$ days
Calculate Number of People: Calculate the number of people required to complete the work in the new deadline. $\newline$ Number of people needed $= \frac{\text{Total work}}{\text{New deadline}}$ $\newline$ Number of people needed $= \frac{600 \text{ person-days}}{12 \text{ days}}$ $\newline$ Number of people needed $= 50 \text{ people}$
Calculate Additional People: Calculate how many more people are needed in addition to the original $40$ people. $\newline$ Additional people needed = New number of people - Original number of people $\newline$ Additional people needed = $50$ people - $40$ people $\newline$ Additional people needed = $10$ people

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