To determine how many lego planes Johnny can build in 40 minutes given that he can build [tex]\(3 \frac{1}{2}\)[/tex] lego planes in 60 minutes, let's break down the problem step-by-step:
### Step 1: Understand the rate of lego plane building
First, convert the mixed number [tex]\(3 \frac{1}{2}\)[/tex] to an improper fraction:
[tex]\[ 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \][/tex]
Johnny can build [tex]\(\frac{7}{2}\)[/tex] lego planes in 60 minutes.
### Step 2: Determine the rate per minute
Next, we need to find out how many lego planes Johnny can build in one minute. To do this, we divide the total number of lego planes by the total number of minutes:
[tex]\[ \text{Rate per minute} = \frac{\frac{7}{2} \text{ planes}}{60 \text{ minutes}} = \frac{7}{2} \times \frac{1}{60} \][/tex]
Simplify the fraction multiplication:
[tex]\[ \frac{7}{2} \times \frac{1}{60} = \frac{7}{120} \][/tex]
So, Johnny builds [tex]\(\frac{7}{120}\)[/tex] lego planes in one minute.
### Step 3: Determine the number of planes in 40 minutes
Now, to find out how many planes Johnny can build in 40 minutes, we multiply the rate per minute by 40:
[tex]\[ \text{Planes in 40 minutes} = \frac{7}{120} \times 40 \][/tex]
Simplify the multiplication:
[tex]\[ \frac{7 \times 40}{120} = \frac{280}{120} \][/tex]
Next, simplify the fraction [tex]\(\frac{280}{120}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor (GCD). The GCD of 280 and 120 is 40.
[tex]\[ \frac{280 \div 40}{120 \div 40} = \frac{7}{3} \][/tex]
So, Johnny can build [tex]\(\frac{7}{3}\)[/tex] lego planes in 40 minutes.
### Step 4: Simplify the final answer
Convert [tex]\(\frac{7}{3}\)[/tex] back to a mixed number for clarity:
[tex]\[ \frac{7}{3} = 2 \frac{1}{3} \][/tex]
Therefore, in 40 minutes, Johnny can build [tex]\(2 \frac{1}{3}\)[/tex] lego planes.
### Conclusion
Johnny can build around [tex]\(2 \frac{1}{3}\)[/tex] lego planes in 40 minutes.
