Let’s solve the two questions visible in the image.

Question 31

If two men can paint a fence in 6 hours, how many hours will it take three men to paint it, assuming they all work at the same rate?

Solution

The total work can be expressed as the product of the number of workers and time:

$\text{Work} = \text{Number of Workers} \times \text{Time}$

1. Calculate the total work: Two men working for 6 hours means: $\text{Work} = 2 \times 6 = 12 \, \text{man-hours.}$

2. Time for three men: Now, divide the total work by three men: $\text{Time} = \frac{\text{Work}}{\text{Number of Workers}} = \frac{12}{3} = 4 \, \text{hours.}$

Answer: D) 4 hours

Question 32

Four workers can do a job in 14 days. How long would seven workers, working at the same rate, take to do the same job?

Solution

Using the same principle as above:

1. Calculate the total work: Four workers working for 14 days means: $\text{Work} = 4 \times 14 = 56 \, \text{worker-days.}$

2. Time for seven workers: Divide the total work by seven workers: $\text{Time} = \frac{\text{Work}}{\text{Number of Workers}} = \frac{56}{7} = 8 \, \text{days.}$

Answer: A) 8 days

Do you want more details or have any questions about the steps?

Related Questions:

1. If 5 workers can complete a task in 10 days, how long would 2 workers take to complete it?
2. If 3 machines can produce 150 items in 5 hours, how many hours would it take 5 machines to produce the same amount?
3. What is the total work required if 10 people complete a task in 4 hours?
4. How does the work rate change if one of the three workers in Question 31 stops working midway?
5. If workers work at half their original speed, how would the answers to Question 31 and 32 change?

Tip:

When solving "rate of work" problems, remember the formula:
$\text{Time} = \frac{\text{Total Work}}{\text{Rate of Work}}.$