Proportions with Complex Fractions Johnny can build \( 3 \frac{1}{2} \) lego planes in 60 minutes. How many can he build in 40 minutes? Simplify your answer completely.

To find out how many lego planes Johnny can build in 40 minutes, we first determine his building rate. If Johnny can build \( 3 \frac{1}{2} \) planes in 60 minutes, we convert \( 3 \frac{1}{2} \) to an improper fraction: \( 3 \frac{1}{2} = \frac{7}{2} \) planes. His rate per minute is: \[ \frac{7/2 \text{ planes}}{60 \text{ minutes}} = \frac{7}{120} \text{ planes per minute} \] Now, we multiply this rate by 40 minutes to find the total planes built: \[ \frac{7}{120} \times 40 = \frac{7 \times 40}{120} = \frac{280}{120} \] Simplifying \( \frac{280}{120} \) gives: \[ \frac{280 \div 40}{120 \div 40} = \frac{7}{3} \text{ planes} \] So, Johnny can build \( 2 \frac{1}{3} \) planes in 40 minutes. For a bit of fun, did you know that the world record for building Lego structures was set in 2017, when a group used 2.5 million Lego bricks to create a 10-foot tall replica of a famous landmark? Imagine how many planes Johnny could’ve built if he had all that time and Lego! Speaking of time, you might want to double-check your calculations to avoid common mistakes, like misreading the fractions or messing up the simplifications. Always take a moment to review your steps, and you'll be flying through these problems in no time!