To determine how many feet the green pepper plants can grow in one month, let's follow these steps carefully:
1. Convert the growth in inches to feet:
Given that the plants grew 5 inches in [tex]\(\frac{3}{4}\)[/tex] month, we need to first convert these inches to feet.
Since [tex]\(1\)[/tex] foot [tex]\(= 12\)[/tex] inches, the growth of 5 inches in feet is calculated as:
[tex]\[
\text{Growth in feet} = \frac{5 \text{ inches}}{12} = \frac{5}{12} \text{ feet}
\][/tex]
2. Calculate the time fraction in months:
The given duration is [tex]\(\frac{3}{4}\)[/tex] month.
3. Determine the growth per full month:
To find out how much the plants can grow in a full month, we need to extrapolate the growth rate discovered.
The rate of growth in feet per month is found by dividing the growth in feet by the time fraction in months:
[tex]\[
\text{Growth per month} = \frac{\text{Growth in feet}}{\text{Time fraction in months}} = \frac{\frac{5}{12} \text{ feet}}{\frac{3}{4} \text{ months}}
\][/tex]
4. Simplify the expression:
To divide by a fraction, we multiply by its reciprocal. Therefore, we have:
[tex]\[
\text{Growth per month} = \frac{5}{12} \times \frac{4}{3}
\][/tex]
Multiply the numerators and denominators:
[tex]\[
\text{Growth per month} = \frac{5 \times 4}{12 \times 3} = \frac{20}{36}
\][/tex]
Simplify [tex]\(\frac{20}{36}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\[
\frac{20 \div 4}{36 \div 4} = \frac{5}{9} \text{ feet}
\][/tex]
Therefore, at this rate, the green pepper plants can grow approximately [tex]\(\frac{5}{9}\)[/tex] feet in one month.
