Questions: A construction company needs 3 weeks to construct a family room and 2 days to add a porch. Write the ratio of the time it takes for constructing the porch to the time it takes for constructing the family room as a fraction in simplest form.

Solution Steps

To find the ratio of the time it takes to construct the porch to the time it takes to construct the family room, we first need to convert all time measurements to the same unit. Since the family room construction time is given in weeks, we will convert the porch construction time from days to weeks. Then, we will express the ratio as a fraction and simplify it to its simplest form.

To find the ratio of the time it takes to construct the porch to the time it takes to construct the family room, we first need to convert the time for constructing the porch from days to weeks.

Given:

• Time to construct the porch = 2 days
• Time to construct the family room = 3 weeks

Since there are 7 days in a week, we convert 2 days to weeks:

\[ \text{Time in weeks} = \frac{2 \text{ days}}{7 \text{ days/week}} = \frac{2}{7} \text{ weeks} \]

Now, we calculate the ratio of the time it takes to construct the porch to the time it takes to construct the family room.

\[ \text{Ratio} = \frac{\text{Time for porch}}{\text{Time for family room}} = \frac{\frac{2}{7} \text{ weeks}}{3 \text{ weeks}} \]

To simplify the ratio, we divide the fractions:

\[ \frac{\frac{2}{7}}{3} = \frac{2}{7} \times \frac{1}{3} = \frac{2 \times 1}{7 \times 3} = \frac{2}{21} \]

Final Answer