In a factory, 4 people can pack 20 boxes in 1 hour. How long does it take 3 people to pack 20 boxes? Give your answer in hours and minutes.

Steps to Solve

1. Determine the rate of work for 4 people

Given that 4 people can pack 20 boxes in 1 hour, we first calculate the rate of work per person.

The rate of 4 people can be expressed as: $$ \text{Rate of 4 people} = \frac{20 \text{ boxes}}{1 \text{ hour}} = 20 \text{ boxes} \text{ per hour} $$

Thus, the rate for one person is: $$ \text{Rate per person} = \frac{20 \text{ boxes}}{4 \text{ people} \times 1 \text{ hour}} = 5 \text{ boxes per hour} $$

2. Calculate the rate for 3 people

Now that we have the rate for one person, we can find the rate for 3 people by multiplying the rate per person by 3: $$ \text{Rate for 3 people} = 3 \times 5 \text{ boxes per hour} = 15 \text{ boxes per hour} $$

3. Determine the time it takes for 3 people to pack 20 boxes

To find out how long it takes for 3 people to pack 20 boxes, we can use the formula: $$ \text{Time} = \frac{\text{Total Work}}{\text{Rate}} $$

Substituting the values: $$ \text{Time} = \frac{20 \text{ boxes}}{15 \text{ boxes per hour}} = \frac{20}{15} \text{ hours} = \frac{4}{3} \text{ hours} $$

4. Convert hours to hours and minutes

To convert $\frac{4}{3}$ hours into hours and minutes, we recognize that: $$ \frac{4}{3} \text{ hours} = 1 \text{ hour} + \frac{1}{3} \text{ hour} $$

Since 1 hour equals 60 minutes, we calculate: $$ \frac{1}{3} \text{ hour} = \frac{60 \text{ minutes}}{3} = 20 \text{ minutes} $$

Thus, the total time is: $$ 1 \text{ hour and } 20 \text{ minutes} $$