Question

1. twenty - five people did $\frac{1}{5}$ of a job in 8 days. then, due to an emergency, the rest of the job must be completed in the next 20 days. how many additional people need to join the project in order to finish in that time frame?

Explanation:

Step1: Calculate work rate per person

Let 1 person's 1-day work = $r$.
Total work done: $25 \times 8 \times r = \frac{1}{5}$
Solve for $r$:
$r = \frac{1}{5 \times 25 \times 8} = \frac{1}{1000}$

Step2: Find remaining work

Remaining work = $1 - \frac{1}{5} = \frac{4}{5}$

Step3: Let total people needed = $n$

Work equation: $n \times 20 \times r = \frac{4}{5}$
Substitute $r = \frac{1}{1000}$:
$n \times 20 \times \frac{1}{1000} = \frac{4}{5}$

Step4: Solve for total people $n$

$n = \frac{4}{5} \times \frac{1000}{20} = 40$

Step5: Calculate additional people

Additional people = $40 - 25 = 15$

Answer:

15