Read, analyze, and solve.

 

14 personnel were assigned to do a task. They were able to finish the task in 5 days. At the same rate, in how many days would the task be finished if there were 20 personnel?

Select one:

a.
1.02


b.
1.1523


c.
28


d.
3.5

To solve this problem, we can use the concept of work rate. The total amount of work done is a product of the number of workers, their rate, and the time taken to complete the task.

Let's denote:

- \( W \) as the total work required to complete the task.
- \( R \) as the rate at which one worker completes the task.
- \( n_1 = 14 \) is the number of personnel in the first scenario.
- \( t_1 = 5 \) is the time taken in the first scenario.
- \( n_2 = 20 \) is the number of personnel in the second scenario.
- \( t_2 \) is the unknown time in the second scenario.

### Step 1: Determine the rate of work

From the first scenario, the total work \( W \) can be expressed as:

\[
W = n_1 \times R \times t_1
\]

Substituting the known values:

\[
W = 14 \times R \times 5 = 70R
\]

### Step 2: Set up the equation for the second scenario

Using the second scenario:

\[
W = n_2 \times R \times t_2
\]

Substituting the values and setting the equations equal since the total work \( W \) is the same:

\[
70R = 20 \times R \times t_2
\]

### Step 3: Solve for \( t_2 \)

Divide both sides by \( 20R \):

\[
t_2 = \frac{70R}{20R} = \frac{70}{20} = 3.5
\]

### Final Answer

The task would be finished in **3.5 days** if there were 20 personnel.

**Correct answer:**

**d. 3.5**

Would you like further details, or do you have any questions?

### Related Questions:
1. What would happen if the number of personnel doubled?
2. How does the completion time change if personnel are reduced by half?
3. If the task's complexity increased, how would the completion time be affected?
4. What would the completion time be if 28 personnel were assigned?
5. How does the work rate per person affect the overall completion time?

**Tip:** When the number of workers increases, the completion time decreases proportionally if the work rate per person remains constant.

14 personnel were assigned to do a task. They were able to finish the task in 5 days. At the same rate, in how many days would the task be finished if there were 20 personnel?

Solve how many days it would take for 20 personnel to finish a task that 14 personnel completed in 5 days, using the work rate and proportionality concept. Suitable for Grades 7-9, learn the mathematical approach to work rate problems with a step-by-step explanation.

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