Question
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The team with the greater unit rate paints more square meters per h \( 2.5>2 \) The Blue Team paines faster. Show how to solve the problem in the Example by comparing the hours per square meter.

Ask by Chen Guerrero. in the United States
Mar 19,2025

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Tutor-Verified Answer

Answer

The Blue Team paints faster because they can cover more square meters in one hour.

Solution

1. The unit rate tells us how many square meters a team can paint in one hour. For the Blue Team, the unit rate is \(2.5\) square meters per hour, and for the other team, it is \(2\) square meters per hour. 2. To compare the painting speeds by using hours per square meter, we find the reciprocal of each unit rate. This tells us how many hours it takes to paint one square meter. 3. For the Blue Team, the hours per square meter is calculated as: \[ \text{Hours per square meter for Blue Team} = \frac{1}{2.5} = 0.4 \text{ hours per square meter.} \] 4. For the other team, the hours per square meter is: \[ \text{Hours per square meter for other team} = \frac{1}{2} = 0.5 \text{ hours per square meter.} \] 5. Since \(0.4 < 0.5\), the Blue Team takes less time to paint one square meter compared to the other team. 6. Thus, the Blue Team paints faster because they require fewer hours per square meter.

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The Deep Dive

To determine which team paints faster, we can convert their rates into hours per square meter. For the Blue Team, if they paint 2.5 square meters in one hour, it means it takes them \( \frac{1}{2.5} = 0.4 \) hours to paint one square meter. Meanwhile, the Red Team paints 2 square meters in one hour, which translates to \( \frac{1}{2} = 0.5 \) hours per square meter. Since 0.4 hours (Blue Team) is less than 0.5 hours (Red Team), the Blue Team indeed paints faster! When solving problems like this, ensure you're comparing the same units. Always convert rates into a common format, like hours per square meter or square meters per hour. Beginners often forget to perform this conversion, leading to inaccurate conclusions about efficiency. Keep an eye on your units for a smooth sailing through rate comparison!

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