Work Problems (Engineering Mathematics)
Problem: Mr. Aw Adi recruited 10 people for the job. For 5 days the 10 people worked, but at the beginning of the sixth day, 3 persons left. How long will it take to finish the job if it’s estimated that 10 people can finish the job in 20 days?
Given formula:
\( nT = t_i n + t_r x \)
Where:
\(x\) = remaining number of people
\(n\) = total number of people supposed to work
\(T\) = estimated time of work if \(n\) people work together
\(t_i\) = initial time where \(n\) people work together
\(t_r\) = remaining time needed to finish the job
Solution:
\( 20(10) = 5(10) + t_r(10 - 3) \)
\( 200 = 50 + 7t_r \)
\( t_r = 21.42 \text{ days} \)
Total time:
\( T_{total} = 5 + 21.42 = 26.42 \text{ days} \)